U.S. stocks jumped 3 percent on Monday, extending gains into a second week as a pledge by German and French leaders boosted hopes that the euro-zone debt crisis may be resolved.

The gains lifted the S&P 500 above its 50-day moving average for the first time since late July, a bullish technical signal. The S&P 500 is now up about 11 percent since its low on Tuesday, when it briefly fell into bear-market territory.

Financials, the most beaten-down stocks during the recent slide, led the rally. The KBW bank index <.BKX> jumped 5.3 percent, with JPMorgan Chase & Co up 4 percent to $31.94 and Bank of America gaining 4.9 percent to $6.2.

The gains, however, came on the second-lightest day of trading since July and may not be indicative of a long-term trend. The advance has been driven by short-covering and managers buying stocks as they try to catch up to the sharp rally built on headlines out of Europe.

There's basically a rally coming off deeply oversold levels, said Fred Dickson, chief market strategist at The Davidson Cos. in Lake Oswego, Oregon.

What's happening is traders are shorting the dollar, and using funds there, and piling into risk-based assets, including equities, he said. The euro, with which the S&P 500 has had a strong correlation, rose the most in 15 months against the dollar.

German Chancellor Angela Merkel and French President Nicolas Sarkozy promised on Sunday to unveil a comprehensive new package to ease the euro zone's debt crisis.

Earnings season is set to begin with Alcoa's report tomorrow after the closing bell and will likely become a driver for stocks in coming weeks.

The Dow Jones industrial average <.DJI> surged 330.06 points, or 2.97 percent, to end at 11,433.18. The Standard & Poor's 500 Index <.SPX> climbed 39.43 points, or 3.41 percent, to 1,194.89. The Nasdaq Composite Index <.IXIC> shot up 86.70 points, or 3.50 percent, to close at 2,566.05.

The S&P 500's next resistance levels are 1,200 and 1,230.

Adding to optimism that there may be a resolution of the euro zone's problems, a move to nationalize Franco-Belgian bank Dexia was seen as an indication that governments would step in and keep large lenders from failing.

The energy and materials sectors also ranked among the day's strongest-performing sectors, while the Dow Jones Transportation Average <.DJT> gained 3.9 percent. Tech provided another source of strength, with the Philadelphia semiconductor index <.SOX> up 2.8 percent.

The materials and energy sectors are forecast to have had the highest earnings growth rates for the third quarter, Thomson Reuters data showed. Shares of aluminum company Alcoa, which is one of the 30 Dow industrials, jumped 3.9 percent to $10.09.

Volume was lighter than average, possibly affected by the U.S. Columbus Day holiday. Government offices and the Treasury bond market were closed for the holiday.

About 6.82 billion shares were traded on the New York Stock Exchange, NYSE Amex and Nasdaq for the day, below the year's daily average so far of 8.03 billion.

Advancing stocks outnumbered declining ones on the NYSE by a ratio of nearly 11 to 1, while on the Nasdaq, advancers beat decliners by nearly 5 to 1.

(Reporting by Caroline Valetkevitch; Additional reporting by Rodrigo Campos; Editing by Jan Paschal)