Stocks surged late in trading on Tuesday as buyers latched onto another report of agreements to strengthen the euro zone's rescue fund to bid up stocks aggressively.

All three major indexes rose sharply after a Britain's Guardian newspaper said France and Germany will increase the euro zone's rescue fund to 2 trillion euros as part of a plan to resolve the sovereign debt crisis.

Investors and buyers piled into financial shares, which had started the day weak but gained momentum on the late news. Shares of Bank of America rose 10.1 percent to $6.64 and trading volume for the Direxion Financial Bull 3X ETF jumped to the highest since April 2010.

The development from Europe is really what we had been rallying on for the past two weeks before Germany yesterday signaled that the issue wasn't quite resolved, said Larry Peruzzi, senior equity trader at Cabrera Capital Markets in Boston.

But the direction of the market can easily reverse if we get something bad again from Europe.

Stocks may also be affected on Wednesday by Tuesday's late news from tech bellwether Apple Inc .

Stock index futures sold off after the bell following weak quarterly results from Apple. Its shares lost more than 5 percent to below $400 in extended trade after the company reported a rare miss in quarterly results after sales of its flagship iPhone fell short of Wall Street expectations. The stock had closed up 0.5 percent at $422.24 during the regular session.

S&P 500 futures fell 6.3 points while Nasdaq 100 futures lost 18.75 points.

Bank of America shares on Tuesday had been lower after it reported a third-quarter profit but showed its main businesses struggled as income from lending and investment banking fell.

Goldman Sachs Group Inc added 5.5 percent to $102.25 after reporting a rare loss, but Goldman said it was moving to cut costs, including employee pay.

Trading picked up shortly after the Guardian report, with 3 billion shares exchanging hands in the final hour on the New York Stock Exchange, NYSE Amex and Nasdaq. A total of 8.86 billion shares traded for the day, above the year's daily average so far of about 8 billion.

Any news out of Europe is a cue for people to jump in or get out of the market. There was a lot of short covering during the final hour, said Stephen Massocca, fund manager at Wedbush Morgan in San Francisco.

The Dow Jones industrial average <.DJI> ended up 180.05 points, or 1.58 percent, at 11,577.05. The Standard & Poor's 500 Index <.SPX> was up 24.52 points, or 2.04 percent, at 1,225.38. The Nasdaq Composite Index <.IXIC> was up 42.51 points, or 1.63 percent, at 2,657.43.

Shares of Yahoo Inc dropped more than 3 percent to $15.96 in extended trading after the company reported its net revenue and profit slipped in the third quarter.

But Intel Corp shares rose nearly 5 percent to $24.54 after the company forecast quarterly revenue above Wall Street's expectations, defying concerns that the growing popularity of tablets and a shaky economy are eating into demand for personal computers.

The CBOE Volatility Index VIX <.VIX>, Wall Street's fear gauge, was down nearly 5 percent but still remained elevated above 30.

Financial stocks were the top gainers. The KBW bank index <.BKX> advanced 5.6 percent.

U.S. homebuilder stocks were helped by strong homebuilder sentiment data, signaling improvement in the housing market.

Shares of KB Home rose 11.6 percent to $7.02.

(Reporting by Angela Moon, Editing by Kenneth Barry)