New York's main contract, light sweet crude for delivery in July, increased 66 cents to close at 72.03 dollars per barrel.

In London, Brent North Sea crude for July delivery climbed 46 cents to 71.05 dollars per barrel in closing deals.

Markets were shut on Monday owing to public holidays in Britain and the United States.

"With little else to focus on, the markets (have) resumed fretting over the Iranian nuclear dispute," said Bank of Ireland analyst Paul Harris.

The market is concerned that Iran -- the world's fourth biggest producer of crude -- could halt exports should the United Nations impose sanctions on the Islamic republic over its disputed nuclear program.

Phil Flynn at Alaron Trading said the market was confused about the news over Iran.

Flynn said there are "worries that a showdown is in store, yet there is news that Iran will restart talks."

Iranian Foreign Minister Manouchehr Mottaki said Tuesday that his country was willing to restart negotiations immediately with the European Union over its nuclear enrichment program.

Iran insists its nuclear program is strictly for civilian energy production but the West suspects Tehran is planning to build nuclear weapons.

Turning to China, Barclays Capital analyst Kevin Norrish said that Tuesday's price gains were also explained by continued strong Chinese oil demand growth.

"According to customs data, Chinese apparent demand grew by 6.3 percent in April," Norrish said.

"Chinese oil demand is most likely to continue at a similar pace for the rest of the year underpinned by a positive economic outlook and the recent rise in retail product prices."

Market participants are, meanwhile, awaiting Wednesday's latest snapshot of US crude inventories.

All eyes will be on gasoline or petrol stockpiles amid the start of the summer driving season when demand for motor fuel peaks as Americans take to their vehicles on vacation.

Elsewhere, the 11-nation Organisation of Petroleum Exporting Countries meets in the Venezuelan capital Caracas on Thursday, with analysts expecting it to stick with its production quota of 28 million barrels of oil per day, owing to the high level of crude prices.

"We do not expect any change in output policies, despite the calls to reduce production by the usual hawkish cadre," said John Kilduff at Fimat USA.

"Don't mistake OPEC's inaction for irrelevance; a serious consideration of output reductions would further rally prices, as global demand remains strong."

Traders were also preparing for the start of the Atlantic hurricane season, which begins on Thursday.

Last year hurricanes Katrina and Rita ravaged US oil facilities along the coast and in the Gulf of Mexico, sending crude futures to then-record highs.

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