World stocks rose on Monday after Greece's parliament passed drastic austerity measures to avoid a chaotic debt default, but doubts over whether Athens will be able to live up to its promises and secure a new rescue package killed an initial rally in the euro.

U.S. crude oil prices closed more than 2 percent higher after Greece on Sunday approved sweeping budget cuts in exchange for a 130 billion euro bailout from the European Union and the International Monetary Fund.

But concerns emerged over whether the country will be able to fulfill its tough austerity promises, keeping demand steady for safe-haven U.S. Treasuries and driving the euro lower.

Unrest in the streets of Athens and a voting rebellion by lawmakers of the ruling coalition suggested Greece may be on the brink of massive social unrest, which would make it difficult for Athens to stick to the rescue terms.

You got that knee-jerk positive reaction (in the euro), and that's ultimately starting to fade, said Brian Dolan, chief currency strategist at Forex.com.

Investors are worried that Greece may fail to meet the targets it's setting itself, and that we're going to be seeing a replay of this several months down the road, he added.

The euro edged 0.1 percent lower against the dollar to $1.319, after rising as high as $1.328 earlier.

On Wall Street, bank shares led U.S. stocks higher, after the S&P 500 on Friday posted its largest decline so far this year. The S&P is up more than 25 percent from its October lows.

That the (Greek) deal was approved really reduces a lot of the tension over the euro zone, but it was expected and on a short-term basis we're very done to the upside, said Yu-Dee Chang, chief trader of ACE Investments in McLean, Virginia.

That's why we went up and then backed off this morning. I'm cautious because there could be a short-term correction.

The Dow Jones industrial average <.DJI> ended 72.81 points, or 0.57 percent, higher at 12,874.04, while the Standard & Poor's 500 Index <.SPX> rose 9.13 points, or 0.68 percent, to 1,351.77. The Nasdaq Composite Index <.IXIC> gained 27.51 points, or 0.95 percent, to 2,931.39.

World stocks climbed 0.75 percent according to the MSCI All-Country World Index <.MIWD00000PUS>, while Europe's FTSEurofirst 300 <.FTEU3> index of top shares ended up 0.71 percent. The STOXX Europe 600 Banks index <.SX7P> closed up 0.5 percent after being up more than 1 percent earlier.

Emerging market stocks jumped 1.1 percent according to a benchmark MSCI index <.MSCIEF>.

U.S. crude oil Climbed 2.27 percent to settle at $100.91 a barrel.

INVESTORS CAUTIOUS

Bond investors remained cautious, however, with Treasuries prices seesawing between negative and positive during most of the session.

Prices of benchmark 10-year U.S. Treasury notes were up 2/32 points late in the day, sending their yield down to 1.97 percent.

Fueling investor concern is a March 20 deadline for Greece to meet debt repayments of 14.5 billion euros. The ruling coalition of Prime Minister Luca Papademos needs to secure bailout funds before that, but EU leaders want to see details on how the promised budget savings will be achieved.

The focus is now on Wednesday's meeting of euro-zone finance ministers, who are supposed to decide on the rescue package.

Prices of U.S. municipal bonds were unchanged after President Barack Obama proposed limiting tax breaks given to high-earners who invest in those securities.

I don't know how much traction (Obama's proposal) is going to get, said Dan Berger, senior market strategist at Municipal Market Data, a unit of Thomson Reuters. If there's any impact on munis it's going to be very small. We'll have to see how the Street reacts to this; they may treat it as the same recycled idea from last year.

(Additional reporting by Luciana Lopez, Chuck Mikolajczak and Joan Gralla; Editing by Kenneth Barry, Andrea Evans, Leslie Adler and Dan Grebler)