Stocks rose on Monday as sentiment swung toward hope that European officials would find a way to cut Greece's debt and shore up European banks.

Shares rallied to session highs in the afternoon after a report said a plan to leverage money from the European Financial Stability Facility was in the works.

Investors were reluctant to make long-term commitments because of conflicting reports about whether or not European officials were preparing to take bold new action to solve the crisis.

Given how markets have behaved over the past two months, people are interested in the vaguest of rumors because any kind of action being taken would be well-received, said Michael Church, president of Addison Capital in Yardley, Pennsylvania.

Markets have been highly sensitive to European efforts to cauterize the euro zone's credit crisis that has Greece teetering near a default. Last week, the Dow had its biggest weekly loss since October 2008 in the depths of the financial crisis, while the S&P 500 shed 6.6 percent for the week.

Financial shares ranked among the session's best performers, with the KBW Bank Index <.BKX> up 5.3 percent. Dow component JPMorgan Chase & Co advanced 7 percent to $31.65 while Citigroup Inc gained 7 percent to $26.72.

However, the Nasdaq's gains were limited after a report on Apple suggested the tech company was cutting back on some key orders.

Talk of plans for a 50 percent write-down in Greek debt and improvements in the euro-zone rescue fund buoyed the market, although European officials called the talk premature. A CNBC report cited a top European official, who said the plans involved using leverage and the European Investment Bank to buy sovereign debt to save European banks.

The Dow Jones industrial average <.DJI> shot up 272.38 points, or 2.53 percent, to end at 11,043.86. The Standard & Poor's 500 Index <.SPX> jumped 26.52 points, or 2.33 percent, to finish at 1,162.95. The Nasdaq Composite Index <.IXIC> climbed 33.46 points, or 1.35 percent, to close at 2,516.69.

The CBOE Market Volatility index <.VIX> fell 5.4 percent but remains more than 20 percent higher for the month.

These confidence issues make it hard to move forward and will result in more volatility ahead, said Mark Foster, who helps manage $500 million at Kirr Marbach & Co in Columbus, Indiana.

Apple slipped 0.3 percent to $403.17 after an analyst said the iPhone maker was cutting orders from suppliers of parts for its iPad tablet. The tech bellwether fell as much as 3.2 percent earlier in the session.

If things slow down on the tablet side, that means that perhaps Apple isn't immune from the economic slowdown after all, Foster said.

On the upside, Boeing Co gave a major lift to the Dow a day after the manufacturer delivered its long-awaited Dreamliner jet to its first airline customer. The stock rose 4.2 percent to $62.01.

Warren Buffett's conglomerate, Berkshire Hathaway Inc , will launch a share-buyback program, an unprecedented move from Buffett that comes after months of investor complaints that the stock was undervalued.

Shares of Berkshire Hathaway's more actively traded Class B stock soared 8.6 percent to $72.09.

In economic news, sales of new single-family home sales fell in August to a six-month low in another sign the U.S. economy is flagging.

About 8.75 billion shares traded on the New York Stock Exchange, the American Stock Exchange and the Nasdaq, above last year's daily average of 8.47 billion.

About 11 stocks rose for every four that fell on the New York Stock Exchange, while about 62 percent of Nasdaq issues rose.

(Reporting by Ryan Vlastelica; Editing by Kenneth Barry and Jan Paschal)