There’s no doubt that President Biden and former President Donald J. Trump will be their respective parties’ nominees, and neither will face credible challengers, but Tuesday’s primaries could be the ones that make it official.

A strong performance today could officially give Mr. Trump a majority of delegates in the Republican National Convention, and Mr. Biden could do the same on the Democratic side.

Georgia, Hawaii, Mississippi and Washington state vote on the Republican side. Voting for Democrats are Georgia, Mississippi, Washington and the Northern Mariana Islands, and Democrats abroad will complete their weeklong trial.

Republicans in the Northern Mariana Islands will vote on Friday, followed by Republicans in Guam on Saturday.

Most states voting this week are holding presidential elections only, with primaries for Congress, governorships and other ballots scheduled for the spring or summer. Mississippi is an exception: the primaries in the Senate and House of Representatives will also be up for vote there on Tuesday.

The Israeli government on Sunday approved a resolution rejecting all international attempts to impose a Palestinian state on Israel, saying Israel should negotiate a “permanent” settlement directly with the Palestinians.

The largely symbolic move followed recent comments from some Israeli allies suggesting they might consider simply recognizing a Palestinian state ahead of an agreement between Israel and the Palestinians.

Prime Minister Benjamin Netanyahu, who presented the resolution to his cabinet, described its adoption as a “declarative decision” that was necessary “in light of comments recently heard in the international community.”

The resolution — which reinforces a position Netanyahu has taken several times in recent days — comes as the Biden administration tries to strike a deal to normalize ties between Israel and Saudi Arabia. U.S. and Saudi officials have said the prospect of that depends on whether Israel agrees to work toward a two-state solution — that is, the creation of a Palestinian state alongside Israel.

Mr Netanyahu has rejected recent pressure from President Biden to agree to that path after the war in Gaza is over, and in recent weeks has doubled down on his opposition to the creation of a Palestinian state.

The final wording of the Israeli government's resolution appeared to be carefully crafted to accommodate both ultranationalist members of Netanyahu's right-wing government, who oppose the idea of ​​negotiations with the Palestinians, and the centrists who join the government have joined. helping monitor the war in Gaza following the October 7 Hamas-led attack.

It did not explicitly rule out the possibility of a Palestinian state, but instead focused on the process.

“Israel completely rejects international dictates regarding a permanent settlement with the Palestinians,” the resolution read, adding: “A settlement, if one is to be reached, will be achieved exclusively through direct negotiations between the parties, without prior conditions.”

David Cameron, the British Foreign Secretary, said last month that a top priority is to give the Palestinian people “a political horizon so that they can see that there will be irreversible progress towards a two-state solution and, crucially , the creation of a Palestinian country.” state.” That led to speculation that Britain might be willing to initiate talks on formal recognition of Palestinian statehood.

After meeting on Friday with King Abdullah II of Jordan, President Macron of France said: “Recognition of a Palestinian state is not a taboo for France.” It was unclear whether Macron was referring to France's long-standing support for a two-state solution in general, or the idea of ​​giving early recognition before a negotiated deal between the Israelis and the Palestinians is reached.

The Israeli government's decision concluded that the unilateral recognition of a Palestinian state in the aftermath of the October 7 attacks would “provide a huge and unprecedented reward for terrorism and prevent any future peace settlement.”

Benny Gantz, the leader of the centrist party who joined Netanyahu's government in October, said Sunday that the normalization process with Saudi Arabia was an important effort he was trying to advance. But in a speech at a conference in Jerusalem, Mr. Gantz added that he “would like to emphasize to our friends around the world: after October 7, the path to regional stability and peace is not through unilateral actions such as the recognition of a Palestinian state that has not reached an agreement in advance with the State of Israel.”

Gabby Sobelman reporting contributed.

Chris Christie, the former governor of New Jersey who was overshadowed by Donald J. Trump in the 2016 presidential primaries, filed paperwork Tuesday saying he would seek the 2024 Republican nomination, set up a rematch with the former president and the field of GOP candidates.

In his second run for president, Mr. Christie, 60, has positioned himself as the person most willing to defeat both Mr. Trump, his former friend-turned-opponent, and Florida Governor Ron DeSantis, who is second in line. to attack. for months in almost every public Republican primary. Mr. Christie’s presence in the race could be unwelcome to Mr. DeSantis, for whom any additional candidate hurts his ability to consolidate support.

Mr. Christie, set to announce his participation Tuesday night at a New Hampshire town hall-style event, has already begun building an aggressive case against Mr. Trump based on the former president’s policies — namely that he made some promises that he never kept. That case is one that other hopefuls have generally sidestepped, instead largely avoiding Mr. Trump’s name. In contrast, Mr. Christie has gone straight to him.

He has mocked Mr Trump’s dwindling mob, calling him a loser and saying he crossed a line with his actions that led to a pro-Trump mob attacking the Capitol on January 6, 2021.

And he has described himself as able to secure the nomination. “I am the viable alternative to Trump,” Christie recently said The everyday beast.

Still, Mr. Christie’s road to winning the nomination is complicated. He’s a Northeast Republican who hasn’t gotten caught up in the culture wars of the Trump era. His main path would necessarily pass through New Hampshire, a state where he ran a fierce campaign in 2016 but ultimately came up short. And to gain traction, he will have to rely on the attention of candidate debates.

His campaign will depend heavily on media coverage and the agility to travel to places where it is most likely. New Hampshire is the state where he will start his campaign, but not necessarily where he will settle.

He still has to meet the Republican National Committee’s criteria to get on that debate stage, which includes 40,000 unique donors.

But if he makes it, as a former friend of Mr. Trump, he has a great understanding of the former president and how to get under his skin. Depending on how the race goes, Mr. Christie’s main impact could be to seriously damage Mr. Trump, whom he has vehemently attacked. But he’s been cheered on by a number of Republican donors and senior officials in recent weeks, especially as Mr. DeSantis stumbled before he even became a formal candidate.

Mr. Christie, a former federal prosecutor, will be in a unique position to attack Mr. Trump’s various legal problems as he is the first former president to be indicted and may face additional charges in other cases.

Still, Mr. Christie will face questions about his conversion from Trump supporter to slanderer. (Mr. Trump called Mr. Christie “an opportunist” after he left office.)

Mr. Christie was a favorite of some Republicans to run for the nomination in the 2012 campaign, when he was one of the most famous governors in the country, known for his dealings with union leaders and selling himself as knowing how to manage a budget had to balance. But instead of running that year, as his star rose, he chose to focus on running for re-election, drawing national attention for his response during the devastating Hurricane Sandy — and criticism from some Republicans for running with President Barack Obama appeared in New Jersey. days before the election at an event related to the aftermath of the storm.

The anger among Republicans foreshadowed a political environment in which Republicans punished their elected officials for their friendship with Democrats.

By the time Mr Christie announced his candidacy for the presidency in 2015, when there was no longer a Democratic incumbent, his candidacy had been hampered by the so-called Bridgegate political revenge scandal that engulfed his government two years earlier. Mr. Christie denied involvement in the alleged repayment plan that saw lanes closed on the George Washington Bridge to retaliate against a political opponent of the governor, and convictions against two defendants were overturned by the US Supreme Court in 2020. But by then, Mr. Christie’s political fortunes had been damaged.

After dropping out of the 2016 race, Mr. Christie endorsed Mr. Trump in February, one of the first prominent national Republicans to do so. That endorsement was valuable to Mr. Trump when he tried to appeal to Republicans who were skeptical of him because of his comments calling for a ban on Muslims entering the country, or his misogynistic statements about the Fox News host. Megan Kelly.

Former Vice President Mike Pence filed paperwork on Monday announcing his presidential candidacy, beginning a long-running campaign against the former president he served under, Donald J. Trump.

Mr. Pence, who has filed the necessary paperwork to serve on the Federal Elections Commission, has entered the single digits in every public inquiry held to date, far behind Mr. Trump, who has served the Republican Party for the past seven years reformed.

The former vice president is expected to formally announce his campaign at a rally in Des Moines on Wednesday, one day after former Gov. Chris Christie is expected to enter the race and the same day North Dakota Gov. Doug Burgum will run.

Pence plans to campaign extensively in Iowa, the first nominating state and a place where his conservative stances on issues such as abortion could appeal to evangelical voters.

Advisers to Mr. Pence, a former Indiana governor, see Iowa as geographically welcoming to the kind of conservatism he practiced before the Trump era. And he’s wagering that enough remnants of the old Republican Party will remain to give his message broad appeal.

Mr. Pence, whom the celebrity-obsessed Mr. Trump used to refer to as “out of central casting,” was a staunch supporter and defender of Mr. Trump as his running mate during the second half of the 2016 presidential campaign, at a time when the Mr. Pence faced a tough re-election run in Indiana.

He was Mr. Trump’s most loyal advocate during their joint tenure.

But Mr. Trump began a pressure campaign on Mr. Pence to prevent Joseph R. Biden Jr.’s Electoral College victory. was certified after Mr Trump lost the 2020 election. Mr. Pence declined to use his ceremonial role as overseer of certification at the U.S. Capitol on Jan. 6, 2021, to further Mr. Trump’s goals.

That day, a pro-Trump mob attacked the Capitol, with some of Mr. Trump’s supporters chanting, “Hang Mike Pence!” Since then, the break between the two has become irrevocable.