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NEW YORK — You can almost hear Wall Street exhaling.

The Dow Jones industrial average soared more than 300 points Thursday after Republican leaders and President Barack Obama finally seemed willing to end a 10-day budget standoff that has threatened to leave the U.S. unable to pay its bills.

The news drove the Dow to its biggest point rise this year and ended a three-week funk in stocks. It also injected some calm into the frazzled market for short-term government debt.

Republican leaders said Thursday they would vote to extend the government’s borrowing authority for six week. A spokesman for Obama said the president would “likely” sign a bill to increase the nation’s ability to borrow money so it can continue paying its bills.

“Congressmen and women are coming to terms with how calamitous it would be if the debt ceiling was not raised,” said Joseph Tanious, Global Market Strategist for J.P. Morgan Asset Management. “Cooler heads are prevailing.”

The Dow jumped 323.09 points, or 2.2 percent, to close at 15,126.07, its high for the day.

The final surge came even as Senate Majority Leader Harry Reid said Democrats would not negotiate with Republicans as long as the government remains partly shut. Reid’s comments were reported about 15 minutes before the market closed at 4 p.m. Eastern time.

Stocks have steadily declined since mid-September as Washington’s gridlock got investors worried that the U.S. could default on its debt and wreak havoc on global financial markets. While traders applauded a potential deal between the White House and Congress, more volatility could be ahead if it falls through.

“We don’t need some grand bargain, we just need to avoid a default,” said Brian Reynolds of chief market strategist at Rosenblatt Securities. “Just don’t bring us to the edge again.”

The Standard & Poor’s 500 index rose 36.16 points, or 2.2 percent, to 1,692.56 and the Nasdaq composite rose 82.97 points, or 2.3 percent, to 3,760.75.

Thursday’s gains were extraordinarily broad. Of the 500 stocks in the S&P 500 index, only 11 fell. Banks and industrial stocks rose the most.

A possible compromise between the two political parties could not come soon enough. Treasury Secretary Jack Lew has said the government will hit its borrowing limit on Oct. 17. That would leave the U.S. with enough cash to last just a week or two before a default became a real risk.

A short-term extension of the debt limit is “the right approach,” said Jack Ablin, who manages $66 billion as chief investment officer at BMO Private Bank.

“It allows politicians to turn down the heat a bit while still keeping the broader issues on the front burner,” Ablin said.

In another bullish signal, small-company stocks rose even more than the rest of the market. Those stocks tend to be riskier than large, well-established companies but can also offer investors greater rewards. A sharp increase in small-company stocks means investors are more comfortable taking on risk. The Russell 2000 index jumped 26.04 points, or 2.5 percent, to 1,069.50. It is less than 20 points from an all-time high reached on Oct. 1.

There were also hopeful signs in the market for short-term U.S. government debt. The yield on the one-month Treasury bill eased to 0.21 percent from 0.27 late Wednesday.

The yield had spiked from near zero at the beginning of the month to as high as 0.35 percent Tuesday as investors dumped the bills out of concern that the government might not be able to pay them back when they’re due. Investors demand higher yields when they perceive debt as being risky.

In other government bond trading, the yield on the 10-year Treasury note edged up to 2.68 percent, from 2.67 percent late Wednesday.

Still, the yield on the longer-term note has fallen in the past month. The move suggests that investors see any potential default as a short-term phenomenon and are predicting that economic growth will remain subdued in the long term.

Nike Inc., Boeing Co. and American Express Co. rose more than 3.4 percent, leading advances among large companies. Wells Fargo & Co. and JPMorgan Chase & Co. gained at least 2.7 percent before reporting earnings today. Gilead Sciences Inc. jumped 6.5 percent as the largest biotechnology company by market value said the cancer drug idelalisib improved survival times.

The Chicago Board Options Exchange Volatility Index, the gauge of S&P 500 options prices known as the VIX, slumped 16 percent to 16.48 for its biggest retreat since April. The gauge is down 8.6 percent in 2013.

Time Warner Cable Inc. jumped 6.1 percent to $116.95. The cable company and Univision Communications Inc., a media group that caters to Hispanic Americans, agreed to extend their partnership and deliver more content to Time Warner subscribers.

Bloomberg News contributed to this report.