U.S. stocks rallied on Tuesday as market sentiment was boosted by refreshed hopes that Greece may have more chances to stay in the euro zone.

When the market closed, the Dow Jones industrial average gained 125.86 points, or 1.01 percent, at 12,580.69. The Standard & Poor' s 500 was up 14.60 points, or 1.11 percent, to 1,332.42. The Nasdaq Composite Index gained 33.46 points, or 1.18 percent, to 2, 870.99.

Stocks traded higher across the board after Greek polls published over the weekend showed a pro-euro zone party was taking the lead ahead of next month's elections, which erased concerns that the country's exit will lead to financial turmoil in the region.

Investors were also expecting China to launch some new stimulus measures to prevent the economy from further slowing down.

However, concerns over Spain still haunted the market. Yields of Spanish bonds surged to 6.5 percent on Tuesday, underlining concerns over the country's ability to bailout its debt-ridden banks.

Adding to the fears, the rating agency Egan-Jones on Tuesday downgraded Spain's credit rating to B from BB-, saying potential bailout of Spain's banks hurt the country's credit.

According to Stephen J. Guilfoyle, U.S. Economist Meridian Equity Partners Inc., questions remain over the Spanish nationalization of Bankia, and Spain's ability to handle the rest of the troubled banking sector.

Stocks hold on gains in spite of gloomy domestic economic data. U.S. home prices were still struggling, with three major indices ended the first quarter of 2012 at the lowest levels since the housing crisis emerged in mid-2006, but showed some signs of stabilization, according to a Standard & Poor's report on Tuesday.

A separate report from the Conference Board showed U.S. consumer confidence fell to a four-month low in May, after a slight decline in previous month.

Some investors believed it was a short-covering rally. "Europe is going to continue to dominate," said Adrian Day, president of Adrian Day Asset Management. "After declines in the market for several weeks, I won't call this sellers exhaustion, but sometimes you run out of sellers at certain prices."

Among companies in focus, Facebook hit a new low on Tuesday, falling below 30 dollars a share for the first time since its much- awaited debut, and closed at 28.84 dollars a share.

In other markets, the U.S. dollar traded mixed against major currencies in late New York trading as the euro continued to decline, while crude prices erased early gains and settled slightly lower as European debt woes weighed.

Light, sweet crude for July delivery slipped 10 cents, or 0.11 percent to settle at 90.76 dollars a barrel on the New York Mercantile Exchange.