Mr. Obama, who met secretly with Speaker John A. Boehner at the White House on Sunday to try to advance the talks, called House and Senate leaders from both parties to the White House for further negotiations on Thursday. And he rejected talk of an interim deal that would get the government past a looming deadline on raising the federal debt limit without settling some of the longer-term issues contributing to the government's fiscal imbalances.

“We've got a unique opportunity to do something big, to tackle our deficit in a way that forces our government to live within its means,” he said in an appearance in the White House briefing room, casting himself as much an honest broker as a partisan participant in the talks. “This will require both parties to get out of our comfort zones, and both parties to agree on real compromise.”

Mr. Obama's previously undisclosed Sunday meeting with Mr. Boehner suggests that the talks are entering a critical phase. There were also intense staff-level negotiations between the White House and Congress over the details of a multi-trillion-dollar package of spending cuts that could clear the way for a vote to raise the debt ceiling, constrain the growth of government and radically reshape the role of government in American society.

The two sides remain in a deadlock over the president's insistence that the package contain tax increases as well as spending cuts. While Mr. Obama did not retreat from that demand Tuesday, he coupled it with a pledge to take on spending in “entitlement programs,” a promise likely to unsettle many Democrats.

While a broad-based agreement may appeal to the White House, neither Senate Republicans nor Democrats may be as eager to embrace one. Democrats worry that a deal that cuts Medicare could rob them of what they see as their political advantage on the issue; Republicans trying to win the majority next year might not like an agreement that is seen as giving Democrats credibility on reducing the deficit.

But Mr. Boehner, while again saying that higher taxes were a nonstarter, expressed pleasure at Mr. Obama's willingness to single out entitlements. “I'm pleased the president stated today that we need to address the big, long-term challenges facing our country,” he said in a statement.

The speaker's session with Mr. Obama was their first face-to-face encounter since the talks presided over by Vice President Joseph R. Biden Jr collapsed last month, officials with knowledge of the meeting said, though the speaker and the president also met privately just before those discussions broke up.

The substance of their talks was not disclosed. But Mr. Boehner's meeting was evidently made known to other House and Senate Republican leaders.

Mr. Obama said the two sides needed to reach a deal within two weeks to pass legislation before August 2, when the Treasury Department says the government risks defaulting on its debt. And he restated that Congress should not procrastinate and let negotiations “come down to the last second.”

Senate Republicans have suggested in recent days that a “mini-deal” be struck, which would allow the government to get past the August 2 deadline but leave the larger fiscal choices to be thrashed out in the 2012 election.

The president rejected that, saying: “I don't think the American people sent us here to avoid tough problems. That's, in fact, what drives them nuts about Washington, when both parties simply take the path of least resistance.”

Still, Mr. Obama eased his tone noticeably from his feisty news conference last week, in which he compared the work habits of lawmakers unfavorably with those of his daughters, Malia and Sasha.

“It's my hope that everybody's going to leave their ultimatums at the door, that we'll all leave our political rhetoric at the door,” he said.

Mr. Obama also eschewed a populist tone, making no reference to “millionaires and billionaires” or owners of corporate jets, even as he spoke of the necessity of eliminating tax breaks and loopholes.

The budget impasse is dominating the White House and Congress. With Republicans protesting that the Senate should be concentrating on fiscal issues this week, Senator Harry Reid, the Nevada Democrat and majority leader, conceded the point on Tuesday and abruptly called off a planned debate on Libya.

After complaints by Republicans that their Fourth of July break had been canceled to deal with the debt-limit fight and not Libya, Mr. Reid essentially threw in the towel and said the Senate would instead take nonbinding votes later this week on how to address the debt-limit dispute.

“Notwithstanding the broad support for the Libya resolution, the most important thing to focus on this week is the budget,” Mr. Reid said.

Senator Mitch McConnell of Kentucky, the Republican leader, restated his opposition to any budget deal containing new taxes. He accused Democrats of a “cheap attempt” at making Republicans look bad by saying that Republicans refused to consider ending a tax break for corporate jets.

Senate Democratic leaders last week called off their planned Fourth of July break due to the August 2 deadline. But the budget talks are occurring mainly off the floor in leadership offices and at the White House so Mr. Reid scheduled the bipartisan Libya resolution for floor debate.

This story “Obama Summons GOP and Democratic Leaders for Deficit Reduction Talks” originally appeared in The New York Times.