Watch our Top Story, "Bailout on the ropes", and our Debate, "Crisis strikes Europe".

Read Douglas Herbert's commentary and our coverage of the effects of the crisis on French banks.

Wall Street roared back on Tuesday, a day after its worst sell-off in 21 years as investors bet Washington would revive a plan to stabilize the U.S. financial sector following its surprising defeat on Monday on Capitol Hill.

Adding to the positive tone was a Reuters report that U.S. regulators intend to provide new accounting guidelines that could slow the heavy flow of mortgage-related losses on banks' balance sheets. The Dow jumped 485 points after posting a one-day record loss of 778 points on Monday.

Strains persisted in credit markets, however, suggesting banks remain reluctant to lend to each other, and September marked the benchmark S&P 500's worst month in six years.

But investors were feeling more optimistic after President George W. Bush and congressional leaders pledged to continue talks on a $700 billion financial-sector rescue plan.

The S&P 500 rose more than 5 percent, recovering more than half of the losses booked on Monday when the House of Representatives rejected the plan, which would have let the U.S. Treasury buy bad mortgage debt from stressed banks so they can resume lending.

Tuesday's climb marked the S&P's best one-day percentage gain since July 2002.

"The president's saying that they'll get something passed this week has definitely calmed nerves," said Marc Pado, market strategist at Cantor Fitzgerald & Co in San Francisco.

"And if a bill doesn't pass, a change in accounting rules might be enough to break the lock in credit markets," he added. "It won't support us forever, but it will buy time and break the stranglehold on the banks."

Under current rules, banks must value assets based on what they would fetch in a current market transaction. Since prices for mortgage-related assets have long been at distressed levels, banks have been forced to scurry for more capital.

The Dow Jones industrial average rallied 485.21 points, or 4.68 percent, to 10,850.66. The Standard & Poor's 500 Index jumped 58.35 points, or 5.27 percent, to 1,164.74. The Nasdaq Composite Index climbed 98.60 points, or 4.97 percent, to 2,082.33.

For the month of September, the Dow fell 6 percent -- its worst month since June. Tuesday also marked the end of the third quarter, when the Dow fell 4.4 percent. This was the Dow's worst quarter since the second quarter of this year.

This is the Dow's longest quarterly losing streak since 1977-1978.

The S&P 500 lost 9.1 percent in September, its worst month since September 2002. For the third quarter, the S&P 500 finished with a 9 percent loss. This was the S&P 500's worst quarter since the first quarter of 2008.

This is the S&P's longest quarterly loss streak since 2000-2001.

The Nasdaq sank 12.1 percent in September -- its worst month since September 2001, when the Sept. 11 attacks on the United States occurred. For the third quarter, the Nasdaq dropped 9.2 percent. This was the worst quarter for the Nasdaq since the first quarter of this year.

On Tuesday, investors snapped up beaten-down shares across the board, with financial and technology companies among the standouts. Apple Inc contributed the most to the Nasdaq's advance, a day after the iPod's maker led the index to its worst day since the bursting of the Internet bubble in April 2000.

Among financials, JPMorgan shares rose 14 percent to $46.70, making the stock a top boost to the Dow. Shares of Citigroup climbed 15.6 percent to $20.51.

It is not unusual for big sell-offs like Monday's to be followed by a short-term relief rally, Mary Ann Bartels, chief U.S. market analyst at Merrill Lynch, wrote in a note to clients. Of the eight times the S&P fell by at least 8.79 percent, a next-day rally occurred six times, she said.

Between July and September, though, the S&P 500 index posted its worst quarter since the third quarter of 2002 and its biggest monthly drop since September of the same year.

What happens next in Washington, investors said, would be instrumental in providing direction for the broader market.

"I am worried that if there is no plan, then the credit squeeze will get worse and it will be like a boa constrictor has got the economy and just keeps squeezing," said Al Kugel, chief investment strategist at Atlantic Trust in Chicago.

The bailout plan's surprising defeat rattled markets around the globe, with Asian stocks following Wall Street's Monday slide overnight. European shares recovered after Bush's remarks and on data showing improvement in U.S. consumer confidence.

Shares of Apple Inc, a tech bellwether, rose 8 percent to $113.66 on Nasdaq. Shares of Intel Corp climbed 8.5 percent to $18.73 after Piper Jaffray, a brokerage, raised its recommendation on the chip maker's stock.

In economic news, the S&P/Case-Shiller Home Price Index showed further deterioration in housing, with prices of U.S. single-family homes plunging a record 16.3 percent in July.

But both the September Chicago PMI, a measure of manufacturing activity in the U.S. Midwest, and the Conference Board's reading on consumer confidence in September, were stronger than expected, tempering concern about the economy.

About 1.62 billion shares changed hands on the New York Stock Exchange, below last year's estimated daily average of roughly 1.90 billion. On Nasdaq, about 2.37 billion shares traded, well above last year's daily average of 2.17 billion.

Advancing stocks outnumbered declining ones on the NYSE by about 4 to 1. On the Nasdaq, advancers beat decliners by nearly 2 to 1.