The Dow Jones industrial average jumped 140 points, led by banks. Italian bond yields dropped sharply after a new government there introduced new austerity measures aimed at restoring confidence in that country's debt. The euro and commodities prices rose.
The leaders of France and Germany, the two strongest countries in the euro area, pushed for a new European Union treaty that would avert another crisis by forcing fiscal discipline on member countries. Ballooning deficits in Greece, Portugal and Ireland have forced those countries get bailouts from their neighbors.
As more nations near the fiscal precipice, there is greater fear that the stronger nations will be unable to bail out the weaker ones. Investors are hoping that a summit of European leaders this Friday will produce concrete measures for preventing a messy breakup of the euro currency, which is shared by 17 nations. Investors have feared that a disintegration of the euro could cause a sharp recession in Europe that would spread through the world economy.
Yields on Italian bonds dove to their lowest level in a month, suggesting traders believe that Italy is far less likely to default. The main Italian stock index jumped 3 percent
The Dow Jones industrial average rose 143 points, or 1.2 percent, to 12,162 in the first hour of trading. The Standard & Poor's 500 index rose 19, or 1.5 percent, to 1,263. The Nasdaq composite index gained 38, or 1.4 percent, to 2.665.
The gains were broad, lifting 28 of the 30 stocks in the Dow and all 10 industry groups in the S&P 500.
Financials stocks were among the biggest winners. Investors have feared that U.S. banks might be dragged down by their close connections to the unstable European financial system.
JPMorgan Chase & Co. jumped 4.5 percent, the most in the Dow. Bank of America was the second-biggest gainer of the Dow 30, rising 3.7 percent. Citigroup Inc. rose 6 percent, Morgan Stanley 4.3 percent.
Monday's strong gains follow the best week in more than two years for U.S. stock indexes. The S&P 500 rose 7.4 percent last week, the most since March 2009. The Dow jumped 7 percent, the most since July 2009.
Markets are hopeful that, given the gravity of the situation afflicting the euro zone, the German and French leaders will come up with a common proposal for tighter integration on budget matters. Analysts say that such a plan could lead to further emergency aid from the European Central Bank, possibly through the International Monetary Fund.
Italy's borrowing costs pulled back from a level that might have forced the nation to default. Analysts say bailing out Italy would be too costly and would hurt the credit standing of German and France, which have the strongest economies in the euro group.
The yield on the 10-year Italian bond plunged half a percentage point to 5.98 percent. It rose above 7 percent in November, a level at which other nations were forced to take bailouts. By comparison, bond yields in Germany, Europe's largest and most stable economy, are roughly 2 percent.
The euro rose 0.5 percent to $1.3481. Crude oil rose $1.30 a barrel to $102.25 in New York.
In corporate news:
— Gannett Co. leapt 11.8 percent after the media company was upgraded to "buy" from "neutral" by analysts at Lazard Capital Markets.
— Incyte Corp. fell 3 percent after a Citigroup analyst downgraded the drug maker to "neutral" from "buy," saying its new blood-disease drug Jakafi might not work as a long-term treatment.
— SuccessFactors Inc. soared more than 50 percent after the company agreed to be sold to German software company SAP for $3.4 billion. SuccessFactors makes software specializing in human resources tasks. The deal is part of SAP's plan to compete with software rival Oracle Corp.