The US Congress passed the government funding bill on September 30 to ensure that the federal agencies continue running for the next 45 days and avoided a federal shutdown.
A bill that keeps the government funded until mid-November but includes no new aid for Ukraine was approved in the Senate by 88 votes to nine, the BBC reported.
The 45-day resolution was proposed by House Speaker Kevin McCarthy after a rebellion by hard-line fellow Republicans who control the chamber.
Once signed into law, it will avert a disruption of federal services.
A shutdown, which would place tens of thousands of federal employees on furlough without pay and suspend various government services, was slated to begin at 00:01 ET (04:01 GMT) on Sunday.
But in a dramatic turnaround on Saturday afternoon, House Republicans scrambled to pass a temporary funding measure that would keep the government open for 45 more days and make no major concessions on spending levels.
It was backed by more Democrats than Republicans, with as many as 90 Republicans voting against it.
The move was a blow to a small group of right-wing Republicans who have held up negotiations in the chamber with unyielding demands for spending cuts.
The US lawmakers should now wrangle on a separate bill which will provide Ukraine with military assistance of $24 billion that Biden was appealing in the budget, with voting likely to be held early next week.
The hardline Republicans, who defied their own party leadership and continued pressing for deep spending cuts while rejecting temporary funding proposals, triggered the shutdown crisis.
According to President Joe Biden, "We cannot under any circumstances allow American support for Ukraine to be interrupted."
"I fully expect the Speaker will keep his commitment to the people of Ukraine and secure passage of the support needed to help Ukraine at this critical moment," he added.
House Speaker Kevin McCarthy pitched the last-ditch "continuing resolution" as government functions from federal policymaking to military operations to food aid stood on the verge of getting upended and the future of millions of public workers remained uncertain.
"In 45 days we should get our work all done," McCarthy said while offering a hand to the hardliners, and stating, "I welcome those 21 back in."
The group of 21 hardliners had said that they would remove McCarthy as speaker if the House passed a stopgap measure they opposed with the support of Democrats.