Stocks rose in a volatile session on Thursday on hopes Greece's political and financial situation would become clearer and after a surprise interest rate cut in Europe boosted sentiment.

Greek Prime Minister George Papandreou's government, on the brink of collapse, was ready to meet with the opposition on demands for a caretaker government. That threw into doubt plans for a referendum on the EU bailout of Greece.

The vote threatened last week's long-awaited agreement to cut Greek debt and strengthen a euro zone rescue fund and was effectively seen as a referendum on Greece's membership in the euro bloc.

The European Central Bank cut its main interest rate by 25 basis points to 1.25 percent as the euro zone's worsening debt crisis outweighed the concern over persistently high inflation, boosting risk appetite.

Markets have been highly susceptible to large swings as developments in the euro zone quickly move to the front burner and overshadow corporate earnings and U.S. economic data.

Equities' trading was choppy as Mario Draghi, in his first news conference as ECB president, also said the euro zone could slip back into a mild recession by the end of the year.

Right now the market just reacts to whatever rumor and whim is out there, going back and forth. What is Greece going to do? What is Germany going to do? What is Merkel saying, what is the meeting doing? said Cliff Draughn, chief investment officer at Excelsia Investment Advisors in Savannah, Georgia.

Sooner or later Europe will solve the problem. There is going to be some pain in between, but they will solve the problem.

The Dow Jones industrial average gained 133.62 points, or 1.13 percent, to 11,969.66. The Standard & Poor's 500 Index climbed 13.16 points, or 1.06 percent, to 1,251.06. The Nasdaq Composite Index added 31.49 points, or 1.19 percent, to 2,671.47.

The PHLX Europe sector index, which includes major European shares, gained 2.3 percent.

But U.S. retailers fell as many top store chains reported disappointing October sales, indicating consumers were still anxious about the state of the economy.

Abercrombie & Fitch tumbled 22.1 percent to $57.66 for its worst percentage drop since November 2000 after posting third-quarter sales. The Morgan Stanley retail index dropped 1 percent.

(Reporting by Chuck Mikolajczak; Editing by Kenneth Barry)