Oil prices stabilise after sharp fall

* Asian demand seen stable in May around 600 million barrels

* Prices fell 3 pct in previous session

SINGAPORE, May 8 (Reuters) - Oil prices stabilised in early trading on Friday, following a steep fall in the previous session, as the demand outlook in Asia remained healthy despite slowing economic growth.

Oil prices tumbled 3 percent on Thursday as a resurgent dollar erased gains from the past two sessions, and after some U.S. producers said they would ramp up drilling after months of falling activity if prices continued to rise.

Healthy Asian demand data, however, helped stabilize prices on Friday.

Thomson Reuters Oil Research and Forecasts said early indicators showed that seaborne crude flows into Asia would be around 80-82 million metric tonnes (586-601 million barrels) in May, broadly steady with April.

Benchmark Brent crude was up 12 cents at $65.66 per barrel at 0055 GMT. U.S. crude was 8 cents higher at $59.02 a barrel.

Despite the slight increase in prices, some analysts said that the market could be capped around $70 a barrel as there was still an oversupply in crude and U.S. producers, which have sharply reduced drilling in recent months of low prices, could increase production.

“U.S. producers... indicated they would ramp up drilling activity if prices continued to rise,” ANZ bank said in a note.

Editing by Richard Pullin