President Biden will convene the top four congressional leaders at the White House on Tuesday as lawmakers swiftly run out of time to strike a deal to avert another partial government shutdown. The president plans to discuss the urgency of legislation to keep federal funding going past midnight on Friday, as well as his requests for billions of dollars in aid for Ukraine and Israel, said Karine Jean-Pierre, the White House press secretary.

“A basic, basic priority or duty of Congress is to keep the government open,” Ms. Jean-Pierre said. “So, that’s what the president wants to see. He’ll have those conversations.”

The spending bill is being held up by demands from hard-right lawmakers in the House, including measures to restrict abortion access, that many members will not support. Ultraconservatives have brought the government to the brink of a shutdown or a partial shutdown three times in the past six months as they try to win more spending cuts and conservative policy conditions written into how federal money is spent.

The result is that Congress has relied on short-term, stopgap spending bills passed by a bipartisan coalition of lawmakers to keep the government open, putting off a longer-term agreement for weeks at a time. Each time, the Republican speaker has assured his conference that House Republicans would fight to secure more policy victories in the next round of negotiations.

With another pair of funding deadlines approaching at the end of this week and the next week, lawmakers are now laboring to try to reach an agreement to fund the government for the rest of the fiscal year. There is increased urgency to complete the task because the debt ceiling agreement brokered in May by Kevin McCarthy, the speaker at the time, and Mr. Biden would cut federal spending 1 percent across the board on April 30 if Congress cannot reach a governmentwide spending deal before then. Both Democratic and Republican senators are determined to avoid that scenario because the cuts would particularly affect Pentagon spending, though several anti-spending conservatives have said they would prefer that outcome.

Tuesday’s meeting comes after Senator Chuck Schumer, Democrat of New York and the majority leader, announced on Sunday that leaders had failed to reach a deal over the weekend because “House Republicans need more time to sort themselves out.” Speaker Mike Johnson accused Senate Democrats of “attempting at this late stage to spend on priorities that are farther left than what their chamber agreed upon.”

In addition to Mr. Johnson and Mr. Schumer, Mr. Biden will also meet with Representative Hakeem Jeffries, Democrat of New York and the House minority leader, and Senator Mitch McConnell, Republican of Kentucky and the Senate minority leader.

Mr. Biden convened congressional leaders at the White House last month in an effort to break the gridlock over his supplemental aid package for Ukraine and Israel, which also included major immigration policy concessions. The package passed the Senate this month, but Mr. Johnson has refused to bring the $95 billion foreign aid package to a vote in the House.

The government spending package is separate from the Ukraine and Israel funding, but Mr. Biden will make the case for both on Tuesday, Ms. Jean-Pierre said. She declined to say what Mr. Biden planned to discuss with the leaders that would break through the impasse.

“We’ve done these types of meetings before and it has moved the ball,” Ms. Jean-Pierre said, referring to the Senate vote.

“What the president wants to see is we want to make sure that the national security interests of the American people gets put first and is not used as a political football,” she said. “We want to make sure that gets done.”

The first batch of government funding will run out on Friday at midnight, while funding for some agencies including the Pentagon and the State Department will expire on March 8.

The White House has ramped up pressure on Mr. Johnson in recent weeks as Ukraine marked the second anniversary of the Russian invasion. Mr. Biden continues to stress that Russia’s president, Vladimir V. Putin, is a global threat.

Jake Sullivan, Mr. Biden’s national security adviser, said on Sunday that he had spoken with Mr. Johnson and that the speaker had indicated that he would like to pass Ukraine funding, but was “trying to figure out a way to do it.”

“Well, this is one of those instances where one person can bend the course of history,” Mr. Sullivan said during an interview on ABC’s “This Week,” adding that the foreign aid package would pass overwhelmingly with bipartisan support if put up for a vote.

“Right now, it comes down to his willingness to actually step up to the plate and discharge his responsibility at this critical moment,” Mr. Sullivan said. “And history is watching.”