Brent crude futures were up $1.53, or 2.1pc, at $73.30 a barrel by 11:58 a.m. (1558 GMT); it touched its highest level in three weeks. US West Texas Intermediate (WTI) crude futures gained $1.35, or 2.2pc, to $63.37 a barrel.
The Saudi-led military coalition in Yemen carried out several air strikes on the Houthi-held capital Sanaa on Thursday after the Iranian-aligned movement claimed responsibility for drone attacks on two Saudi oil pumping stations earlier in the week.
"You have a sizable strike on Iran-aligned Houthi forces in Yemen today, so until there's some kind of stepback from that situation, this market is going to have a tough time trading lower," said Mizuho director of futures Bob Yawger.
"There's just a lot of political risk in this market."
Saudi Arabia's deputy defence minister accused Iran of ordering the drone attack on the pumping stations.
It comes after attacks on four oil tankers off the coast of United Arab Emirates on Sunday.
Taken together, the escalation of tensions has compounded fears of supply disruption in the Middle East.
US staff was ordered to leave the American embassy in Baghdad on Wednesday out of concern about perceived threats from Iran.
Iraq's oil minister Thamer Ghadhban said Thursday that international oil companies have said they are operating as normal in the country, Iran's direct neighbor.
Asian shippers and refiners have put ships heading to the Middle East on alert and are expecting a possible rise in marine insurance premiums after the attacks.
Japanese Prime Minister Shinzo Abe told Iran's Foreign Minister Mohammad Javid Zarif he was concerned the situation in the Middle East "is becoming very tense."
The market still faces uncertainty over whether the Organization of the Petroleum Exporting Countries (OPEC) and other producers will continue with supply cuts that have boosted prices more than 30pc so far this year.
Ghadhan said the next meeting of OPEC's joint monitoring committee will assess the commitment of member and non-member countries to the production cuts.
OPEC said on Tuesday that world demand for its oil would be higher than expected this year.