The weakening dollar is increasing the chances of a cut in output by oil producers' group Opec at its next meeting later this month.
Opec members buying goods from Europe are paying more
On Monday the dollar hit a 20-month low against both the euro and the pound, denting the revenues of oil exporters which sell the commodity in dollars.
Experts believe most Opec members want another reduction in oil quotas, after opting for an emergency cut in October.
The 1.2 million barrel-a-day cut was the first in two years.
Ministers opted for the cut - which came into effect in November - to help stabilise prices after they fell from a peak of $78.40 a barrel in July to below $60 in October.
But prices have since rebounded. In early afternoon trade US light, sweet crude was at $62.90 a barrel while Brent crude had reached $63.92.
Despite recent rises, most officials from Opec countries are supporting a further cut in output ahead of their meeting in Nigeria on 14 December.
They are concerned about the dollar, which has been steadily falling on the back of fears that the US economy could be contracting.
"Opec is in the process of taking up the challenge of a market that is clearly and steadily getting out of balance, after almost three years of a very strong bull run," said Mohammed Barkindo, Opec's acting secretary general.
While Opec is not seeking a specific oil price, Mr Barkindo said the value of the dollar was a significant factor to be taken into account when determining output.
"We cannot ignore the extremely soft dollar amongst other factors" said Edmund Daukoru, Opec president and Nigerian minister.
But he added that oil stocks were "very high".