The Senate advanced a wartime aid package for Ukraine and Israel, reviving an effort that had stalled amid Republican opposition to a border security bill they demanded and later abandoned.

A day after blocking a measure that would have paired harsh new border restrictions with security assistance for Ukraine and Israel, several Republicans agreed to open debate on a foreign policy version of the bill – after securing the opportunity to propose changes, including the border restrictions that were stripped out.

Like the border deal, the new foreign aid package would pair billions of dollars in military assistance for Ukraine and security assistance for Israel with humanitarian assistance for civilians in Ukraine, Gaza and the West Bank. However, it would not include the US border security measures outlined in the bipartisan measure, although some Republican senators expressed interest in adding border provisions through an amendment process.

Among them was the senator Lindsey Graham, a Republican of South Carolina, who announced his opposition to advancing the funding measure on Thursday “because I believe we have not done all we can to secure our southern border”.

I enthusiastically support Ukraine, Taiwan and Israel, but as I have been saying for months now, we must protect America first,” the Trump ally said in a statement.

Related: Republicans’ standalone Israel aid bill fails in House vote

The Senate held an initial vote on the foreign aid package on Wednesday, in which 58 members supported advancing it. That initial motion required only a simple majority for passage, so the bill was able to advance, but 60 votes were needed for advancement on Thursday.

There was some apparent uncertainty over how much support the bill had on Wednesday, forcing senators to keep the initial vote on the proposal open for four hours as they debated the best path forward. That evening, the Senate majority leader, the Democrat Chuck Schumer of New York, took to the floor to announce that members would reconvene on Thursday to vote on the legislation.

“We will recess until tomorrow and give our Republican colleagues the night to figure themselves out,” Schumer said. “We’ll be coming back tomorrow at noon, and hopefully that will give the Republicans the time they need. We will have this vote tomorrow.”

Schumer’s comments came hours after the Senate voted 49 to 50 against advancing the bipartisan border bill. Sixty votes were required to start debate on the bill, but 44 Senate Republicans and six of their Democratic colleagues blocked the legislation from moving forward. Just four Senate Republicans – including James Lankford, a Republican of Oklahoma, who helped broker the border deal – supported advancing the bill.

Schumer initially supported the bill’s advancement, but he then changed his vote, a procedural maneuver that would allow him to take up the legislation again later. In a floor speech delivered Wednesday before the vote, Schumer criticized Republicans for opposing the bipartisan bill and accused them of doing Donald Trump’s political bidding. The former president had called on Republicans to oppose the border deal out of concern for how it might affect the presidential race and his campaign’s focus on the issue of immigration.

“Donald Trump doesn’t like that the Senate finally reached a bipartisan border deal. So he has demanded Republicans kill it,” Schumer said. “He thinks it’s far better to keep the border in chaos so he can exploit it for personal political gains. And Senate Republicans – vertebrae nowhere to be found – are ready to blunder away our best chance of fixing the border in order to elevate what they see as the interests of Donald Trump above the interests of the country.”