U.S. stocks resumed their rally after hopes of a big bailout for the Eurozone were rekindled.

The S&P 500 Index rallied 24.52 points, or 2.04 percent, to close at 1,225.38. The Dow Jones Industrial Average climbed 180.05 points, or 1.58 percent, to close at 11,577.05. The Nasdaq Composite rose 1.63 percent.

U.S. stocks and other risk assets rallied in the afternoon session on a report from the Guardian that Germany and France have agreed on a measure to expand the power of bailout fund EFSF to 2 trillion euros from 440 billion euros.

Germany and France have also agreed that banks should be recapitalised to meet the 9% capital ratio that the European Banking Authority is demanding.

These two key Eurozone countries will push for their agreement at the upcoming Eurozone meeting on Sunday, reported the paper, citing EU diplomats.

Some analysts and investors expressed doubts over the Guardian report, especially so soon after German Chancellor Angela Merkel cautioned that these sovereign debts have built up over decades, so they won't be ended with one summit.

Dow Jones also reported that the purported 2 trillion euros agreement is totally wrong, citing an official.

Nevertheless, the U.S. stock market clearly extended its rally upon the publication of the Guardian report.

Even before that, U.S. stocks were positive in the morning session, buoyed by the upbeat earnings (albeit clouded by accounting gains and asset sales) from Bank of America (NYSE:BAC), which closed up 10.12 percent on Tuesday.