US West Texas Intermediate (WTI) crude futures CLc1 were at $61.20 a barrel at 0122 GMT, down 16 cents, or 0.2 per cent, from their previous close.
"Meanwhile, the EIA confirmed, or possibly made worse, what we already knew about USA shale output, which is relentlessly marching higher".
Despite the lower rig count, which is an early indicator of future output, activity remains much higher than a year ago when, when just 617 rigs were active, and most analysts expect USA crude oil production, which has already risen by over a fifth since mid-2016, to 10.37 million barrels per day (bpd), to rise further.
Hedge funds and money managers pared their bullish wagers on US crude oil, with long positions falling last week for the first time in three weeks.
During the said week, Organization of Petroleum Exporting Countries (OPEC)'s basket price stood at $63.58 per barrel with $49 cents increase compared to the preceding week.
Crude prices rose on Friday after the USA economy added the biggest number of jobs in more than 1-1/2 years in February. The resulting fallout could drag down crude prices after a rally of more than 40 percent since June, he said.
Elements of the Taliban open to talks with Afghan government, says Mattis
This is Mattis's second visit to the war-torn country after he last visited in September. He said the positive signals had come from small numbers of insurgents.
USA oil production gains nevertheless are offsetting an effort led by the Organization of Petroleum Exporting Countries to cut into the surplus on five-year oil inventories through output curtailments.
On Monday, benchmark 10-year notes last rose 8/32 in price to yield 2.8663 percent, hovering near multi-year highs.
MSCI's world equity index .
Last week's U.S.jobs data, as well as an easing of fears of a global trade war, boosted stocks across many parts of the world.
Emerging market stocks rose 1.21 percent.
The broader trend remained positive for Wall Street's main indexes, which had closed up almost 2 percent on Friday on the strength of the jobs report. S. dollar. The dollar index . A stronger dollar would likely dent oil prices.