Gains were capped by concerns that a prolonged trade war between Washington and Beijing could lead to a global economic slowdown, Reuters reported.
Brent crude futures, the international benchmark for oil prices, were at $72.31 per barrel, up 34 cents, or 0.5 percent, from their last close. US West Texas Intermediate (WTI) crude futures were up 42 cents, or 0.7 percent, at $63.52 per barrel.
"Escalating tensions between the US and Iran, in addition to signs that OPEC will continue its production cut, drove oil higher," said Jasper Lawler, head of research at futures brokerage London Capital Group.
Iraq's oil minister said growing tension in the Middle East poses a challenge to the stability of global crude oil markets and said OPEC must pave the way for a "new agreement" to help stability and support prices. He did not elaborate.
The tension comes amid an already tight market as the Organization of the Petroleum Exporting Countries (OPEC), Russia and other producers withhold 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.
Price gains were constrained by pressure on financial markets, which have this week been weighed down by worries that the United States and China are digging in for a long, costly trade war.