Brent crude oil steadies above $60 after sharp Monday fall

* Traders take on new long positions below $60 a barrel

* High U.S. and Middle East production maintains supply glut

By Henning Gloystein

SINGAPORE, March 3 (Reuters) - Brent crude oil prices steadied above $60 a barrel in early Asian trading on Tuesday, supported by traders entering the market after prices dropped sharply in the previous session on the back of record U.S. stocks.

Brent futures fell 5 percent, its most in a month, on Monday as record stocks and speculation of a nuclear deal with Tehran could lift Iran's sanctions and boost its oil exports brought worries about high supplies back to the market.

But with an immediate lifting of sanctions unlikely, prices lifted again on Tuesday after traders took advantage of cheap oil to take on new long positions.

Front-month Brent crude futures were trading at $60.20 a barrel at 0147 GMT, up 66 cents from their last settlement. U.S. WTI futures were up 28 cents at $48.87 a barrel.

"Brent crude prices (are) attempting to rally on rapid week-on-week reduction in U.S.... rig count," Morgan Stanley (Xetra: 885836 - news) said on Tuesday in a note.

U.S. oil rig count fell by 33 rigs last week. "The current U.S. horizontal and vertical rig count across the Permian, Eagle Ford, Bakken and Niobrara shale plays implies that U.S. oil production growth will reach 385,000 b/d (barrels per day) y-o-y by 4Q15, down 55 kb/d versus last week's rig count," Goldman Sachs said on Monday.

Despite the slowing rig count, U.S. production as well as output in the Middle East remains high, adding to an oversupplied market.

"Saudi, UAE (United Arab Emirates), Iraqi and other Middle East production and exports (are) all higher TYD (to year date)adding to supply pressure," Morgan Stanley said. (Editing by Michael Perry)