Oil rallied more than 4 percent on Monday, rebounding as last week's record double-digit losses attracted bargain hunters and as equities markets remained stabilized after last week's strong U.S. April jobs report.

Crude prices rose even though the dollar index <.DXY> erased early losses after a ratings downgrade for Greece by Standard & Poor's weighed on the euro.

Sturdy U.S. gasoline futures, especially the June front-month contract as the summer driving season approaches, also provided lift for crude futures.

Brent crude for June rose $4.43 to $113.56 a barrel by 12:04 p.m. EDT (1604 GMT), well off its earlier $109.05 low.

U.S. crude for June rose $3.89 a barrel to $101.07, having reached $101.22.

The Reuters-Jefferies CRB index <.CRB>, a global benchmark for commodities prices, rose 1.8 percent after last week posting its biggest weekly drop since late 2008, down 9 percent.

We went through a pretty hefty sell-off for all markets, said Tony Machacek, an oil trader at Bache Commodities. It smacked of funds getting sell-stops triggered. Now that long liquidation has been done, everything seems to be stabilizing.

But analysts and traders expressed caution about the rebound in oil prices.

After such a big fall last week, a bounce by crude prices is to be expected, but the question is whether it will just be a dead-cat bounce, or dead-barrel bounce as I call it, said Phil Flynn, analyst at PFGBest Research in Chicago.

Flynn noted concerns about geopolitical risk revived by unrest in Egypt and Syria over the weekend.

The euro fell for a fourth straight day, building on a strong sell-off last week. Euro zone debt worries continued to mute any bounce in the single currency, particularly after the downgrade of Greece.

Standard and Poor's cut Greece's credit rating further into junk territory, reflecting growing doubts that the euro zone's most fragile economy can manage its debt without imposing losses on private bondholders.

U.S. stocks edged up as concerns over European debt offset gains in natural-resource shares lifted by the commodities bounce. <.N>

The euro zone problems have bearish implications for dollar-denominated crude prices not only because they pressure the euro and lift the dollar, but because Europe's oil demand may be curbed.

(Additional reporting by Claire Milhench in London and Francis Kan in Singapore; Editing by Dale Hudson)