Brent crude futures, the international benchmark for oil prices, rose 1 cent to $71.98 a barrel by 11:01 a.m. EDT (1501 GMT).

US West Texas Intermediate (WTI) crude futures were unchanged at $63.21 a barrel, as the WTI contract for June delivery expired. The July contract was trading at $63.19 a barrel.

"The two powerful countervailing forces in the market right now are the Iran tensions versus the deteriorating US-China trade war situation," said John Kilduff, a partner at Again Capital LLC in New York.

The trade war "really hits the Asian economies and the demand outlook, and this situation with Iran has the market on tenterhooks at the same time," Kilduff said.

On Monday, US President Donald Trump threatened Iran with "great force" if it attacked US interests in the Middle East.

Washington suspects that militia with ties to Iran organized a rocket attack in Iraq's capital Baghdad.

On Tuesday, Iran said it would resist US pressure, declining further talks under current circumstances.

Iraq's oil minister said a growing conflict in the Middle East poses a challenge to the stability of crude oil markets and said the Organization of the Petroleum Exporting Countries (OPEC) must pave the way for a "new agreement" to help stability.

Tensions have mounted during an already tight market as the OPEC, Russia and other producers have withheld supply to support prices.

Saudi Arabia has signaled its willingness to continue curbing output until the end of the year. OPEC will meet at the end of June or in early July.

Also adding to market tightness was the closure of a major pipeline in Nigeria and supply disruptions from Russia.

The prolonged tariff fight between the United States and China, however, raised concerns about a global economic slowdown and dampened market sentiment.

Signs that Asian economies were already getting hit by the trade conflict helped to boost the US dollar, making crude more expensive.

The market will watch US crude stockpiles reports on Tuesday afternoon from the American Petroleum Institute (API) and Wednesday morning from the U.S Energy Information Administration (EIA).

Analysts in a Reuters poll said would likely rise by 5.4 million barrels in the week to May 10.