Talks between Republicans and the White House Friday ended with lawmakers cooing about the mood of cooperation that has been lacking in previous rounds of budget talks.
Lawmakers have until Jan. 1 to assemble a budget plan that would replace a mandatory set of spending cuts and tax hikes that economists say would throw the U.S. economy back into recession.
Fears the economy would fall off the "fiscal cliff" have undermined markets that have dropped sharply since before the Nov. 6 election. Both the Dow Jones industrial average and the Standard & Poor's 500 index are down more than 4.5 percent since the election and down 7 percent or more since the recent peak in late September.
Comments after Friday's meeting helped give stocks a boost in Asia and Europe.
By close of trading Monday, the DJIA added 207.65 points or 1.65 percent to 12,795.96. The tech-heavy Nasdaq composite index gained 62.94 points or 2.21 percent to 2,916.07. The S&P 500 tacked on 27.01 points or 1.99 percent to 1,386.89.
On the New York Stock Exchange, 2,728 stocks advanced and 351 declined on a volume of 3.3 billion shares traded.
The benchmark 10-year treasury fell 11/32 to yield 1.617 percent.
The euro rose to $1.2781 from Friday's $1.2743. Against the yen, the dollar rose to 81.34 from 81.31 yen.
In Tokyo, the Nikkei 225 index gained 3.66 percent, 323.48 points, to 9,153.20.
In London, the FTSE 100 index added 2.36 percent, 132.07, to 5,737.66.