Brent oil steady above $108 on Greece hopes, Gulf of Mexico storm

* Greek parliament likely to approve austerity programme

* U.S. crude stocks fall more than expected - API

* Coming Up: EIA oil data, 10:30 a.m. EDT

SINGAPORE, June 29 (Reuters) - Brent crude steadied on Wednesday above $108 a barrel on growing optimism that the debt crisis in Greece will be resolved and underpinned by a tropical storm in the Gulf of Mexico.

U.S. crude held steady near $93 after industry data showed tighter supply at the world's largest oil consumer.

News that tropical storm Arlene continued to head northwest from the Bay of Campeche in the Gulf of Mexico also underpinned oil prices.

ICE Brent crude for August fell 10 cents lower at $108.68 a barrel by 0306 GMT. U.S. August crude rose 8 cents to $92.89 a barrel. Both contracts rose more than 2 percent on Tuesday.

"Investors are taking profits after big gains last night," Tetsu Emori, commodities fund manager at Astmax Investments in Tokyo, adding that once Brent breaks a short-term resistance at $110 a barrel, $115 should be easy to reach.

Brent's premium to U.S. light sweet crude narrowed to $15 a barrel after rising above $17 on Tuesday.

Growing market confidence that the Greek parliament will approve the austerity programme, and that a French plan to rollover Greek sovereign bonds will help avert a default, lifted Asian stocks and the euro.

Greek lawmakers will vote Wednesday and Thursday on a five-year package of spending cuts, tax increases and privatisation in order to secure the next 12 billion euro slice of aid in July.

"Any positive compromise within Europe, with Greece willing to make some sacrifices, will cause the euro and oil to rally," said Jeremy Friessen, a commodity strategist at Societe Generale.

U.S. CRUDE STOCKS

Oil also gained support after industry data showed a larger-than-expected drop in crude stocks and a surprise fall gasoline inventories.

Investors are looking to government data due later on Wednesday for confirmation that oil supply is tightening in the United States.

Yet, concerns about the release of emergency stocks from consumer countries, that caused oil to tumble 7 percent last week, hovered.

"There is still some heaviness in the market in relation to the increase in supply from strategic reserves," Societe Generale's Frissen said.

"The increase in reserves is mostly coming from the United States, which is the most oversupplied market in the world right now."

The country is expected to move away from global fundamentals where supply is expected to tighten in the second half of the year on strong demand, he said.

(Reporting by Florence Tan; Editing by Ed Lanee)