* Firmer oil market comes after week of heavy losses
* U.S. crude holds near $60 per barrel as output soars
* Soaring U.S. output undermines OPEC efforts to prop up prices
* Drivers for higher oil price "unlikely sustainable" - Goldman (Adds Goldman Sachs comments, updates prices)
SINGAPORE, Feb 12 (Reuters) - Oil prices rose by 1 percent on Monday, recovering some of last week's steep losses as Asian stock markets found a footing after days of chaotic trading.
Looming over oil markets, however, was rising production in the United States that is undermining efforts led by the Organization of the Petroleum Exporting Countries (OPEC) and Russia to tighten markets and prop up prices.
Brent crude futures were at $63.54 per barrel at 0728 GMT, up 75 cents, or 1.2 percent, from the previous close.
U.S. West Texas Intermediate (WTI) crude futures were at $60.04 a barrel. That was up 84 cents, or 1.4 percent, from their last settlement.
The stronger prices came after crude registered its biggest loss in two years last week as global stock markets slumped.
But with U.S. equities rebounding on Friday and Asian markets seemingly steadying on Monday, analysts said crude was also supported.
"The bounce in U.S. stocks means some catch-up is possible (for oil)," said Greg McKenna, chief market strategist at futures brokerage AxiTrader.
McKenna said stock markets on Monday were quiet as "the incentive for traders in Australia or Asia to do anything without the lead of the U.S. is likely to be lacking," referring to recent U.S. stock market volatility.
It is also a holiday in Japan.
Oil markets, though, still face soaring U.S. oil production <C-OUT-T-EIA>, which has risen above 10 million barrels per day (bpd), overtaking top exporter Saudi Arabia and coming within reach of top producer Russia.
There are also strong signals the output will rise further.
U.S. energy companies added 26 oil rigs looking for new production this week, boosting the count to 791, the highest since April 2015, General Electric's Baker Hughes energy services said on Friday.
"The increase over the last month has been driven primarily from private producers," U.S. bank Goldman Sachs said in a note to clients on Monday.
As a result, "investor fear around greater U.S. oil production/lack of producer discipline has risen."
The soaring U.S. output is undermining efforts led by OPEC and Russia to push up prices with production cuts that started in 2017 and are set to last through 2018.
In a separate note, Goldman Sachs said "the drivers of higher oil prices from September until last week healthy global demand, voluntary/involuntary supply disruptions and US producer discipline are unlikely to be sustainable."
(Reporting by Henning Gloystein; editing by Richard Pullin and Tom Hogue)