The number of active U.S. rigs drilling for oil has fallen for a record 20 weeks in a row to its lowest since 2010, according to data from oil services company Baker Hughes, fuelling expectations of a drop in U.S. production.
"We believe that the increase in U.S. oil production will slow and that it could also decline in the short term," Germany's Commerzbank said in a note on Monday.
Brent edged up 6 cents to $65.34 a barrel by 1328 GMT (9.28 a.m. ET), having touched a low of $64.60 on dollar strength earlier in the session.
U.S. crude, called WTI, was up 37 cents at $57.52 a barrel, having slipped to $56.71 earlier.
The dollar was trading 0.1 percent higher against a basket of currencies, easing back from 0.3 percent earlier in the day. A strong U.S. currency makes dollar-traded commodities such as crude oil more expensive for holders of other currencies.