The stock market rallied Monday as investors gained confidence that European leaders will address their continent’s debt crisis and fears diminished that the United States will fall back into recession.

The Standard & Poor’s 500-stock index rose 3.4 percent, its best day since August, and the Dow Jones industrial average was up 330 points on the day. European stock markets were up as well, including a 3 percent gain in the German Dax index. The rally extended to Asian markets in early trading Tuesday. Japan’s Nikkei 225 index ended its morning session up 2 percent.

The gains were driven by a sense that European authorities are addressing problems in their banking system head-on. Over the weekend, officials decided to restructure Dexia, one of the continent’s most troubled financial firms, with the Belgian government taking ownership of the bank’s Belgian arm. And France, Belgium and Luxembourg agreed to guarantee that Dexia can get the money it needs to operate.

Meantime, German Chancellor Angela Merkel and French President Nicolas Sarkozy said Sunday that they will have a plan in the coming weeks to recapitalize the European banking system and address Greece’s inability to repay its debts. The leaders promised the plan in time for a Nov. 3 summit of world leaders in Cannes, France.

The steps taken by European policymakers reduced fears that the continent’s crisis could create ripple effects in the U.S. economy.

“The market is ... seeing the two people who are most important in resolving Europe’s problems saying what many of us have been saying as private citizens, which is acknowledging the need to strengthen the banks,” said Jerry Webman, chief economist at Oppenheimer Funds. “That has given markets a bit of comfort that the probability of a major shock to the U.S. economy from Europe has been reduced.”

Investors in recent weeks sold off shares of major U.S. financial firms out of fear they were exposed to troubled European banks, but the strongest gainers on U.S. markets Monday were bank stocks. Bank of America shares rose 6.4 percent Monday, closing at $6.28 a share.

U.S. bond markets were closed for the Columbus Day holiday.