As the rig count fell, "the market is starting to think that USA shale oil production may not steadily grow, which is supporting oil prices", Takayuki Nogami, chief economist at state-backed Japan Oil, Gas & Metals National Corp., said by phone from Tokyo.
"The ever-expanding USA supply continues to pose significant downside risk to oil prices", said Stephen Innes, head of trading for Asia/Pacific at futures brokerage OANDA in Singapore.
U.S. West Texas Intermediate (WTI) crude futures CLc1 were at $61.25 a barrel at 0414 GMT, down 11 cents, or 0.2 percent, from their previous close, Reuters said.
Crude prices rose on Friday and earlier on Monday after the U.S. economy added the biggest number of jobs in more than one-and-a-half years in February.
"Meanwhile, the EIA confirmed, or possibly made worse, what we already knew about USA shale output, which is relentlessly marching higher".
USA production is expected to rise above 11 million bpd by late 2018, taking the top spot from Russian Federation, according to the International Energy Agency (IEA).
After the US boosted rigs drilling for oil for six straight weeks, American explorers idled four rigs last week, easing fears over surging shale production.
Exports have averaged about 1.5 million barrels over the past six months, nearly double the level in the previous six months, Energy Information Administration data show.
U.S. Shale production is expected to rise above 11 million bpd by late 2018, taking the top spot from Russian Federation, according to the International Energy Agency (IEA).
While a brighter economic outlook has underpinned demand expectations, expanding American production remains a challenge to the Organization of Petroleum Exporting Countries and its allies, which are trying to prop up prices via output curbs.
"The average monthly increase (in shale output) in the eight months since September is 155,000 bpd".
"Thus OPEC has no scope to expand production from its current level".
Iran's light crude oil price rose 79 cents in the week ended on March 2 to settle at $63.18 per barrel, Shana news agency reported on Sunday. The U.S. government expects major shale regions to boost output by 131,000 bopd in April, spurring fears that surging supplies will undermine OPEC's efforts to clear a glut.
USA crude inventories probably expanded by 2.5 MMbbl in the week through March 9, according to a Bloomberg survey before EIA data on Wednesday.