By Luke Pachymuthu

SINGAPORE (Reuters) - Oil prices steadied over $126 on Friday, after a steep fall in the previous session, as the dollar's rally overshadowed the biggest drop in U.S. inventories since 2004, while concerns over global energy demand grew.

U.S. crude was down 5 cents at $126.57 a barrel at 9:06 p.m. EDT, after settling $4.41 lower at $126.62 a barrel on Thursday. London Brent fell 13 cents to $126.90 a barrel.

Gains in the U.S. dollar following a report that the U.S. economy grew in the first quarter at a faster pace than previously estimated prompted investors to return to the equities market in the United States.

The dollar held steady near a three-month high against the yen on Friday, in the wake of the upward revision to U.S. economic growth figures that bolstered expectations for the Federal Reserve to raise interest rates this year.

The losses in global oil benchmarks coincided with an announcement by U.S. futures market regulator, the Commodity Futures Trading Commission (CFTC) that it would step up surveillance of energy trading, tracking index funds and reaching across the Atlantic to grab more information on oil contracts based on American crude that are traded in Britain.

"A rebound in the dollar, speculation about U.S. interest rate hikes and the announcement by the CFTC of measures to enhance the oversight of energy futures markets may be seen as potentially stemming future investment flows into energy and other commodities," said Antoine Halff, of Newedge USA LLC, in a research note.

Oil prices briefly rose on Thursday, after a report by the U.S. Energy Information Administration showed an 8.8 million-barrel drop in U.S. crude stockpiles, the biggest fall since a hurricane shut offshore oil platforms in September 2004.

The EIA had said earlier this week that U.S. oil demand in March fell to its lowest level for that month in five years, a fresh signal that consumers are struggling to cope with high oil prices.

Asian countries have started reviewing fuel subsidies, which have sheltered motorists from the shock of steep price rises, intensifying fears of an Asian energy demand slowdown.

On Thursday India's oil minister, Murli Deora, said the government would take a decision on raising fuel prices in the next two to three days.

Taiwan, Indonesia and Sri Lanka have already raised domestic fuel prices.

(Editing by Clarence Fernandez)