Brent crude was down 37 cents, or 0.5%, at $71.12 a barrel by 1335 GMT, after declining 0.6% on Monday. U.S. West Texas Intermediate oil was off by 27 cents, or 0.4%, at $68.96 a barrel, having dropped by 0.6% in the previous session.

"A previous price surge that was probably premature, coupled with a stronger U.S. dollar and a correction on the stock markets, are weighing on oil prices," Commerzbank said.

As oil is priced in dollars, a stronger greenback makes crude more expensive for buyers with other currencies.

Data showing China's crude imports were down 14.6% in May on a yearly basis also weighed on prices.

"China was taking advantage of low oil prices a year ago, so the base is uncharacteristically high," oil brokerage PVM noted.

Heavy Chinese refinery maintenance in May also contributed to the decline.

Crude prices have risen in recent weeks, with Brent up by nearly 40% this year and WTI gaining even more, amid expectations of demand returning as some countries succeed in vaccinating populations against COVID-19.

Restraint on supply by the Organization of the Petroleum Exporting Countries and allies has also helped buttress prices.

"The fundamental environment on the oil market remains favourable: fuel demand is recovering strongly not only in the United States, but also in Europe following the (partial) lifting of restrictions," Commerzbank said.

In Britain, one of the most vaccinated countries in the world, there are now doubts that the country will lift all coronavirus-related restrictions as previously planned on June 21.

Barriers to the revival of Iran's nuclear deal remain ahead of talks due to resume this week between Tehran and world powers, four diplomats, two Iranian officials and two analysts said. 

Iranian demands about sanctions relief and Western concern over Iran's expanding nuclear know-how are among questions that may require weeks or possibly months of further negotiation, the diplomats and analysts said.