The price of oil rose early on Monday as a result of the dollar's fall, but an increase in the number of oil drilling platforms in the United States has raised fears that the global bottleneck of oil supply will continue despite some producers' efforts to cut output.
London Brent crude futures rose 24 cents, or 0.53 percent, to $ 45.78 a barrel at 0047 GMT.
Futures for the WTI rose 21 cents, or 0.49 percent, to $ 43.22 a barrel.
The US dollar index remained low against a basket of currencies as expectations that the US Federal Reserve will raise interest rates again later this year have dwindled. A decline in the dollar makes oil cheaper for countries using other currencies.
Although oil prices rebounded after a 10-month decline, they have been down about 13 percent since late May when OPEC and some other producers agreed to extend an agreement to cut output by 1.8 million bpd by the end of March.
But oil supplies in the United States, which were not part of the OPEC-led deal, have undermined the impact of the cuts.
Data from Baker Hughes Energy Services showed that US energy companies added 11 oil drilling platforms in the week ending June 23 to a total of 758 platforms, the largest since April 2014.