The UK said overnight that the two countries shared a desire to resolve the impasse just hours after Foreign Secretary Margaret Beckett cautioned against hope of a "swift resolution" to the stand-off.
At 11:30 am (0330 GMT), New York's main oil futures contract, light sweet crude for delivery in May, was up 2 cents at 64.66 usd a barrel from 64.64 usd in late US trades.
Brent North Sea crude for May rose 7 cents to 67.88 usd.
Prices had fallen sharply overnight on hopes for an easing of tensions with Iran, dealers said.
"People feel there are some signs that both sides are moving to a peaceful resolution and towards diplomacy. This has brought the geopolitical risk premium in the market down," said Mitsubishi Corp's Tokyo-based energy risk manager Tony Nunan.
He cautioned, however, that this did not mean tensions would ease quickly, noting that Iran remains under international pressure over its nuclear program.
Oil prices have risen over the past week on concerns that Iran, the world's fourth-biggest producer of oil, could move to cut its exports should the crisis with the UK escalate.
Iran's detention of 15 British sailors and marines has further strained relations between Iran and the West at a time of mounting international impatience with the Islamic republic over its refusal to rein in its uranium-enrichment programme. Uranium is a key ingredient for a nuclear bomb, but Iran says its research is meant for peaceful purposes.
To resolve the row over the detained British personnel, the UK has proposed "direct bilateral discussions" and was waiting for Iran's response.
Iran's top security official, Ali Larijani, said the new contacts could create the conditions for ending the stand-off as both sides toned down their rhetoric.
Iran insists the 15 marines and sailors were captured on March 23 because they had illegally entered Iranian waters. The UK claims they were taken while in Iraqi waters.
Meanwhile, the market is looking ahead to the US Department of Energy (DoE) weekly report on energy stocks to be released later today.
Analysts are forecasting a drop in gasoline (petrol) and distillate stocks and a build-up in crude. Gasoline inventories, which have been falling for the past few weeks amid growing demand ahead of the peak US driving season, will be a key figure.
"The refineries are coming out of the spring maintenance season ... we can expect to see a build in gasoline in the next few weeks and fears of insufficient gasoline supply will be alleviated," Nunan said.
