WASHINGTON—The Bush administration and Congress anxiously revived negotiations Friday on a $700 billion financial bailout, one day after the largest bank collapse in U.S. history provided a brutal reminder of the risks of failure.

“I’m convinced that by Sunday we will have an agreement that people can understand on this bill,” predicted Massachusetts Rep. Barney Frank, a key Democrat in eight days of up-and-down talks designed to stave off an economic crisis.

House Speaker Nancy Pelosi added that “progress is being made,” although neither she nor Frank divulged details at a late-afternoon news conference in the Capitol. Talks continued into the evening.

Frank and Pelosi spoke a few hours after President Bush prodded lawmakers to “rise to the occasion”—and quickly.

In one small sign of progress, House Republicans dispatched their second-ranking leader, Rep. Roy Blunt of Missouri, to join the talks after their objections to an emerging compromise had brought negotiations to a standstill the day before. They also demanded “serious consideration” for a plan of their own, involving less government intrusion and lower cost to the taxpayers than the $700 billion that Treasury Secretary Henry Paulson has been seeking.

The legislation the administration is promoting would allow the government to buy bad mortgages and other sour assets held by investors, most of them financial companies. That should make those companies more inclined to lend and lift a major weight off the national economy that is already sputtering. But a significant number of lawmakers, including many House conservatives, say they’re against such heavy federal intervention.

Under their plan, the government would insure the distressed securities rather than buy them. Tax breaks would provide additional incentives to invest.

Democrats and Bush officials said the insurance proposal was acceptable as an option but not as a replacement for the administration’s more sweeping approach.

The crisis was hardly limited to the U.S.

Bush held a lengthy Oval Office meeting with British Prime Minister Gordon Brown that was focused on how the problems were spreading, then said, “I told him the plan is big enough to make a difference, and I believe it will be passed.”

Presidential politics weighed heavily and unpredictably on the election-season effort to stave off a full-blown economic crisis.

After announcing earlier in the week he would suspend his campaign and return to the capital until there was an agreement, Republican John McCain abruptly reversed course and departed for Friday night’s debate with Democratic rival Barack Obama.

“Now that Sen. McCain is safely in Mississippi we can get back to serious work,” sniped Frank, who had challenged the Republican presidential candidate in a White House meeting on Thursday to describe his own solution to the crisis.

There were fresh signs of urgency at both the White House and the Capitol, one day after the unusually tempestuous White House session and the collapse of Washington Mutual, the largest failure in U.S. banking history. The Seattle-based institution had invested heavily in the now-moribund mortgage market.

Still, the Dow Jones industrials rose 121 points for the day as investors anticipated a weekend agreement.

In days of negotiations, the administration has accepted demands from lawmakers to give Congress considerable authority to oversee the bailout. Additionally, Paulson relented to requests to limit the severance packages that corporate executives can receive from firms benefiting from the government bailout.

Also, rather than provide $700 billion upfront, as Paulson initially requested, Congress would approve the funds in stages. Under one approach, $250 billion would be made available at once, with the president able to certify the need for an additional $100 billion on his own authority. The final $350 billion would become available with a second presidential certification, although this time Congress would have authority to block it.

Any compromise is also expected to require the government to obtain partial ownership of any company it invests in.