Oil tried to sustain forays above $81 with Brent briefly jumping over $1 as confidence over a deal to help debt-ridden Greece was tempered by worries the global recovery could still falter and keep crude demand weak.

Euro zone leaders agreed on a safety net for Greece with the International Monetary Fund late on Thursday -- a move which pulled the euro off 10-month lows and revived investor appetite for riskier assets, including commodities.

The EU deal contributed to rising risk appetite, a weaker dollar and thus rising energy prices, said Carsten Fritsch, analyst at Commerzbank.

The euro rallied off a 10-month low against the dollar after the agreement, but the plan did not alleviate longer-term worries about Greece and other fiscally vulnerable economies in Europe, limiting market moves.

U.S. crude for May delivery rose for the first time in three days and bounced over $81 and by 1126 GMT (7:26 a.m. EDT) was up 73 cents to $81.26 per barrel. ICE Brent touched a high of $80.68 and then slipped back to show gains of 88 cents at $80.49.

The European cacophony is not over, said Olivier Jakob at Petromatrix in a note. Trading in (U.S. crude futures) is likely to be dominated again by reaction to the ... plan for Greece, he added.

Commerzbank's Fritsch said financial investors were stepping into the market around $80 as they continued to bet on a rise in demand led by Asia, supported by tentative signs of recovery in the United States as product stockpiles declined.

But the fundamental supply and demand picture remained weak, he added, providing a likely cap of around $83 on prices.

There's still a risk of a large oversupply in the second quarter leading to a further build in stocks, he said, given a rise in U.S. crude oil inventories and signs that OPEC pumped even more oil in the four weeks to April 10.

Oil market players will watch for indications on the U.S. recovery from gross domestic product (GDP) data for the fourth quarter due at 1230 GMT and from a barometer of consumer sentiment for March by the University of Michigan, expected at 1355 GMT (9:55 a.m. EDT).

A report on Thursday showing the number of U.S. workers filing for jobless aid fell sharply last week helped push Japan's Nikkei average higher on Friday, mirroring gains in the Dow and S&P 500.

The initial jobless claims was a very encouraging sign, said Clarence Chu, an energy trader at Hudson Capital Energy in Singapore. If the number of unemployed people drops, it will be a big boost for oil.

(Editing by Sue Thomas)