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

Greece's approval on Sunday of sweeping budget cuts in exchange for a 130 billion euro bailout from the European Union and the International Monetary Fund also drove a jump in U.S. crude oil prices to over $100 a barrel and a 1 percent rise in the Nasdaq on Monday.

But concerns emerged over whether Greece will be able to fulfill its tough austerity promises, keeping demand steady for safe-haven U.S. Treasuries and putting a lid on euro gains. 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 right now, 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 was practically flat against the dollar at $1.320 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 a low in early October.

That the 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> was up 75.91 points, or 0.59 percent, at 12,877.14, while the Standard & Poor's 500 Index <.SPX> gained 9.47 points, or 0.71 percent, to 1,352.11. The Nasdaq Composite Index <.IXIC> was up 26.14 points, or 0.90 percent, at 2,930.02, minutes after jumping 1 percent.

World stocks climbed 0.8 percent according to the MSCI All-Country World Index <.MIWD00000PUS>, while Europe's FTSEurofirst 300 <.FTEU3> index of top shares was up 0.7 percent. The STOXX Europe 600 Banks index <.SX7P> closed up 0.5 percent after being up more than 1 percent earlier.

U.S. crude oil rose 1.7 percent to $100.95 a barrel.

INVESTORS CAUTIOUS

Bond investors remained cautious, however, with Treasuries prices seesawing between negative and positive territories.

Greece needs to secure bailout funds in order to meet debt repayments of 14.5 billion due on March 20.

The focus is now on Wednesday's meeting of euro-zone finance ministers. They may agree in principle on the aid package, but are likely to withhold final approval until it is clear what proportion of Greece's private creditors will agree to take losses.

Prices for benchmark 10-year U.S. Treasury notes were down 2/32 points, sending their yield up to 1.993 percent.

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 and Chuck Mikolajczak in New York, Emelia Sithole-Matarise and William James in London; Editing by Kenneth Barry, Andrea Evans, Leslie Adler)