Wall Street extended a huge rally today 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 industrials rose about 370 points, giving them a massive gain of about 780 over two days, and Treasurys fell as money flowed into equities.

The plan to rescue banks from billions of dollars in bad debt has reassured investors who worried that a continuum of bad bets on mortgages would hobble more financial companies and cause even more damage to the 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,” principal and head of equity trading at The Williams Capital Group., Stephen Carl, said. He added, though, that “it depends on how it’s structured.”

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,” a market strategist at Stifel, Nicolaus & Co., Joe Battipaglia, said.

Treasury Secretary 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 on the plan through the weekend with congressional leaders.

The government’s plan could resolve a year-long credit crisis that intensified this week, pummeling the stock market and forcing lending to grind to a virtual standstill. Wall Street suffered massive losses Monday and Wednesday, and credit markets seized up following this week’s bankruptcy of Lehman Brothers Holdings Inc. and the bailout of teetering insurer American International Group Inc.

The government took other steps today 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 injected another $20 billion in temporary reserves into America’s financial system. The central bank also will buy short-term debt obligations issued by Fannie Mae, Freddie Mac, and the Federal Home Loan Banks.

And to help calm investors’ anxieties, 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 many investors have been fleeing them, fearing that the funds’ holdings included souring corporate debt.

To help limit the freefall in financial stocks, the Securities and Exchange Commission on Friday enacted a temporary ban 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. Those cheaper shares can 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, like those of Lehman Brothers last week. Some say the fundamental problems with the financial stocks 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 Mr. 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 reflect short sellers who are forced to step in and cover their bets by buying now rising stocks that had predicted would fall. While that played some role in the advances yesterday and today, 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.

According to preliminary calculations, the Dow rose 368.75, or 3.35%, to 11,388.44 after having been up as much as 463.36.

Today was a quarterly “quadruple witching” day, which marks the simultaneous expiration of options contracts, an event that often adds to volatility and heavy volume, leading to swings in the major indexes.

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

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

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 0.99% from 0.07% late yesterday. Yields move opposite from price. The yield on the benchmark 10-year Treasury note shot up to 3.80% from 3.53% late yesterday.

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