Senate Democrats have postponed the rescue of an aid bill for Israel and Ukraine for at least a day.

Senate Democrats, who pushed for a standalone bill to send tens of billions of dollars to Israel and Ukraine after Republicans blocked a compromise that would have combined aid with tough border security measures, promised a vote on the alternative Thursday.

In a day full of whiplash on Capitol HillOn Wednesday, Democrats tried to prevent the aid from falling victim to former President Donald J. Trump's political campaign. But after hours of deadlock, Senator Chuck Schumer, Democrat of New York and majority leader, announced that senators needed more time to reach an agreement on how to move forward with that alternative, which both Democrats and Republicans said they hoped it would be successful.

Mr. Schumer had hoped for a quick vote Wednesday on what he called his “Plan B” to revive the aid package after the border deal collapsed. But by Wednesday evening, the action had stalled, as Senate Republicans slowly walked things out onto the floor as they regrouped. They kept a procedural vote open for hours as they sought assurances from Democrats that if they voted to pass the stripped-down relief bill, they would be allowed to propose changes.

After 7 p.m., Schumer said the Senate was retreating to “give our Republican colleagues the night to collect themselves.”

Despite the delay, there were glimmers of hope that the aid package for Ukraine and Israel would eventually make progress. A bipartisan vote to advance the relief package would mark a remarkable turnaround after months of deadlock and likely put the measure on track for Senate approval within days.

The measure would send $60.1 billion to Ukraine for its war against Russian aggression, $14.1 billion in security aid for Israel and $10 billion in humanitarian aid for civilians in global crises, including Palestinians and Ukrainians.

The effort to get the legislation back on track came after Republicans blocked a bill that would tie foreign aid to strict border security measures they had demanded. That plan, which was hammered out over four months of difficult bipartisan negotiations, won bloody Republican support after Trump expressly opposed it. It failed on a 50-49 vote, falling short of the 60 votes that would have been needed to advance, as all but four Republicans voted to reject it.

Even if Democrats manage to revive the relief bill in the Senate, it still faces stiff headwinds in the Republican-led House, where right-wing lawmakers oppose sending additional aid to Ukraine. Some have even threatened to impeach Speaker Mike Johnson if he brings forward a bill that includes this.

Mr. Johnson would not say Wednesday morning whether the House of Representatives would pass the standalone national security bill if and when it passes the Senate. On Tuesday night, Republicans failed to push through a $17.6 billion bill to direct military aid only to Israel, a failure that Mr. Johnson tried to pin on Democrats.

Karoun Demirjian contributed reporting from the Capitol.