International benchmark Brent crude fell slightly to $66.44 at 0712 GMT on Monday, while American benchmark West Texas Intermediate (WTI) saw prices of $58.67.
On Friday at 1400 GMT, Brent crude traded at $66.97 and WTI registered as $59.24 at the same time.
With the U.S. Federal Reserve's remarks, which sent 10-year treasury yields to the lowest level since early 2018, and with concerns over a potential U.S. recession, oil prices fell on Monday.
Global oil prices are trading at around $66 driven higher by the Organization of the Petroleum Exporting Countries (OPEC) and some of cooperating non-OPEC countries oil cuts, as well as by outages in Venezuela and Iran because of U.S. sanctions.
The number of oil rigs in the U.S. fell to 824 for week ending March 22, a drop of nine over the previous week, according to data released by oilfield services company Baker Hughes on Friday.
As the number of oil rigs fell for a fifth straight week, although last week's count was down by just 1, the rig count reached the lowest level since April 2018.
Despite the decrease in the oil rig count and Thursday's Brent price peak of 2019, oil slumped on the global market on Friday, with international benchmark Brent crude closing at $66.86 per barrel while American benchmark West Texas Intermediate finished the day at $59.98 a barrel.
By Gulsen Cagatay