Traders work on the floor of the New York Stock Exchange, where consolidated volume came to a heavy 9.1 billion shares yesterday. The Dow Jones Industrial Average rose 368.75, or 3.35 percent.

BLOOMBERG NEWS / DANIEL ACKER

NEW YORK — Wall Street had another extraordinary rally yesterday as investors stormed back into the market, relieved that the government plans to restore calm to the financial system by rescuing banks from billions of dollars in bad debt.

The Dow Jones Industrial Average rose 368.75, or 3.35 percent, to 11,388.44 after having been up as much as 463.36 giving it a gain of about 780 over two days.

Broader stock indicators also surged. The S&P 500 index rose 48.57, or 4.03 percent, to 1,255.08, and the Nasdaq composite index rose 74.80, or 3.40 percent, to 2,273.90.

Stocks of Rhode Island importance rose, led by Bank of America Corp. and Webster Financial Corp. The Bloomberg Rhode Island Index, a price-weighted list of companies with operations in the region, rose 5.56 to 242.43. Bank of America rose $6.90 to $37.48. Webster rose $5.01 to $28.00.

Yesterday was a quarterly “quadruple witching” day, which marks the simultaneous expiration of options contracts, an event that often adds to volatility and heavy volume. Still, much of the market’s moves were due to the government’s actions yesterday.

The government’s proposal, while still a work in progress, has placated investors who worried that a continuum of bad bets on mortgages would hobble more financial companies and cause further damage to the strained banking system and the overall economy.

“If a solid plan is put in place, it’s definitely going to be a positive in easing the pain,” said Stephen Carl, principal and head of equity trading at The Williams Capital Group. He added, though, that the set-up of any plan will determine its success.

A new government ban on short selling, or placing bets that a stock will fall, likely added to the market’s gains as traders adjusted their positions. “A big chunk of this is scaring all the shorts to cover their bets,” said Joe Battipaglia, market strategist at Stifel, Nicolaus & Co., referring to short sellers.

Treasury Secretary Henry Paulson, speaking about the rescue plan, said a bold approach is needed to remove troubled assets from the books of financial firms. He offered few details, but said he would work through the weekend with congressional leaders to assemble a remedy.

The plan could help neutralize a yearlong credit crisis that intensified this week. Wall Street suffered massive losses Monday and Wednesday, and credit markets essentially seized up after this week’s bankruptcy filing of Lehman Brothers Holdings and the bailout of teetering insurer American International Group.

Analysts said it was the first government response decisive enough to restore confidence in the markets; in the past, the administration has relied largely on steps such as injecting cash into the banking system that had a limited impact.

“Everything they had done had been a Band-Aid approach, at the margins,” said Jay Mueller, economist at Strong Capital Management. “Now we’re dealing with the root problem.”

The government took other steps yesterday to restore stability to the financial system. The Federal Reserve said it will expand its emergency lending and let commercial banks finance purchases of asset-backed paper from money market funds. The Fed also injected more money into the U.S. financial system, as it had done earlier in the week, and said it will buy short-term debt obligations issued by mortgage giants Fannie Mae, Freddie Mac and the Federal Home Loan Banks.

To further ease investors’ anxieties and bolster tattered investor confidence, the Treasury Department has decided to use a Depression-era fund to provide guarantees for U.S. money market mutual funds. Money market mutual funds are typically considered safe, but some investors have been fleeing them, fearing that the funds’ holdings included souring corporate debt.

And to help limit the freefall in financial stocks, the U.S. Securities and Exchange Commission yesterday enacted a ban until next month on the short-selling of nearly 800 financial stocks. Short-selling is the common practice of betting against a stock by borrowing shares and then selling them in the open market. A short-seller’s hope is the stock will fall; if it does, the stock can be bought back at the lower price. The cheaper shares can then be returned to the lender, allowing the investor to pocket the profits. Traders can lose, however, if the stock rises.

Wall Street observers have disagreed over the extent to which pressure from all those bets that a stock will fall shaped investor sentiment and strangled some financial stocks, such as those of Lehman last week. Some say the fundamental problems with overleveraged financial companies warranted the pessimism while others say the short selling was a death knell for some financial names.

“The federal government has been petitioned by Wall Street to take evasive action in the money markets, the stock and bond markets, to avoid a complete meltdown of the credit system,” said Battipaglia. “Once the credit system melts down, the economy falls. We can hand-wring about if this is the proper thing for the government to do, or if Wall Street pulled the panic button too soon, but that’s something for the historians to sort out.”

It’s difficult to quantify how much of the market’s gains reflected short sellers who are forced to step in and cover their bets by buying now-rising stocks that they had predicted would fall. While that appeared to play some role in the advances Thursday and yesterday, the Nasdaq composite index — dominated by big technology stocks, not financials — showed big gains along with the Dow and the Standard & Poor’s 500 index.

Even with yesterday’s big gains, stocks didn’t end the week with much change after the whipsaw sessions.

The Dow ended the week down 33.55, or 0.29 percent, the Standard & Poor’s 500 index finished up 3.38, or 0.27 percent and the Nasdaq composite index ended the week up 12.63, or 0.56 percent.

The Russell 2000 index finished the week up 33.48, or 0.27 percent, at 753.74.

The Dow Jones Wilshire 5000 Composite Index — a free-float weighted index that measures 5,000 U.S. based companies — ended at 12,882.14, up 117.26 points, or 0.92 percent, for the week. A year ago, the index was at 15,371.29.

Treasury prices dropped as investors poured money back into stocks. The yield on the 3-month Treasury bill — a safe investment to which investors have rushed this week — rose to 0.95 percent from 0.07 percent late Thursday. Yields move opposite from price. The yield on the benchmark 10-year Treasury note shot up to 3.81 percent from 3.53 percent late Thursday.

The stock market’s enormous swings during the week reveal how anxious investors have been about the tightness in the credit markets and the possibility that other financial companies might succumb.

There are precedents for a federal takeover.

In the late 1980s, the government created the Resolution Trust Corporation to tackle the savings and loan crisis. It acquired the defaulted mortgages, foreclosed real estate and other assets of nearly a thousand failed S&Ls, restoring order and stability to the system. Resolving that crisis took six years and $125 billion in taxpayer money — roughly equal to $200 billion in today’s dollars.

And there was the Reconstruction Finance Corporation, a Depression-era relief program formed in 1932 by President Hoover that tried to revive the market by giving loans to banks and other businesses.

Yesterday, Treasury Secretary Henry Paulson gave few details about the structure of the new program. Asked about an overall price tag, he said, “hundreds of billions” of dollars.

Congressional leaders said they were ready to move quickly but still needed details of the administration plan. For instance, there was no indication of what the government would get in return from financial companies for the federal assistance.

A grim-faced President Bush acknowledged risks to taxpayers in what would be the most sweeping government intervention to rescue failing financial institutions since the Great Depression. But he declared, “The risk of not acting would be far higher.”

“Every American should know that the federal government continues to enforce laws and regulations protecting your money,” Mr. Bush said at the White House.

The only lasting move in a week of intense volatility came late in Thursday’s session when reports emerged that the government was considering a plan that would shift soured debt off financials’ books. A wobbly market rocketed higher, giving the Dow a 410-point gain for the session, buying that continued through yesterday.

The dollar rose against most other major currencies in trading yesterday, while gold prices jumped. Light, sweet crude oil rose $6.67 to settle at $104.55 a barrel on the New York Mercantile Exchange.

Advancing issues outnumbered decliners by about 7 to 1 on the New York Stock Exchange, where consolidated volume came to a heavy 9.1 billion shares compared with 10.3 billion shares traded Thursday.

The Russell 2000 index of smaller companies rose 30.06, or 4.15 percent, to 753.74.

Overseas stock markets soared. Japan’s Nikkei stock average jumped 3.8 percent, and Hong Kong’s Hang Seng index surged 9.61 percent. In Europe, Britain’s FTSE 100 jumped 8.84 percent, Germany’s DAX index advanced 5.56 percent, and France’s CAC-40 rose 9.27 percent.