Oil prices rose on Tuesday on optimism that Greece can pass an unpopular austerity program as Europe works to fashion a solution to Athens' debt woes, and also on lift from a weak dollar, according to Reuters. The weak dollar boosted oil and other dollar-denominated commodities as the euro rallied on the optimism about Greece's ability to avoid default. The euro got more lift after the Portuguese government said it planned to be scrupulous in meeting terms of a financial bailout. The 19-commodity Reuters-Jefferies CRB index rose by 1.5 percent and headed for its biggest gain since May 25. "Despite the violence in Greece, there is the hope that the austerity plan will be passed. So, that puts Greece on the back burner for now," said Phil Flynn, analyst at PFGBest Research in Chicago. ICE Brent crude for August rose $2.41 to $108.40 a barrel by 12:24 p.m. EDT (1624 GMT), having traded as high as $109.05. U.S. August crude rose $1.17 cents to $91.78 a barrel, having swung between $90.44 to $92.19. Brent's premium to U.S. light sweet crude benchmark West Texas Intermediate stayed on the rebound, pushing above $17 a barrel intraday on Tuesday, after briefly slipping below $13 intraday on Monday. U.S. gasoline and heating oil futures posted stronger percentage gains than U.S. crude, continuing to tag along with the stronger Brent moves ahead of front-month July contracts expirations on Thursday. Brent trading volumes continued to outpace U.S. crude volumes, with Brent on pace to surpass its 30-day average. Greek lawmakers will vote Wednesday and Thursday on a package of spending cuts, tax increases and privatization required by international lenders as a price for further financial aid. Anti-austerity protests turned violent in Athens on Tuesday. The European Union warned Greek lawmakers the country faces immediate default unless they back the unpopular economic plan. Hopes for solving Greece's debt crisis got a boost from news that German banks have agreed in principle to use a French proposal as a basis for negotiating private-sector participation in a Greek debt rollover. France offered a radical solution Monday for banks to roll over some Greek debt for 30 years. U.S. stocks rose on the optimism about Greece, with data showing a moderation in the pace of home price declines in the United States also lending support.