Brent North Sea crude for delivery in June delivery soared to USD 65.13 per barrel.
The contract later stood at USD 64.86 in London late afternoon deals, up USD 2.13 from Wednesday's closing level.
US benchmark West Texas Intermediate for June meanwhile jumped USD 1.78 to USD 57.95 a barrel.
"Crude oil prices rebounded to reach four-month highs following news that Saudi Arabia renewed its aerial assault in Yemen to target the Shiite rebels," said energy analyst Myrto Sokou at the Sucden brokerage in London.
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The Saudi-led coalition's latest strikes in Yemen came despite a demand by rebels for a complete halt to the raids as a condition for UN-sponsored peace talks.
The regional alliance had Tuesday declared an end to the first phase of its operations against the Iran-backed Huthi rebels and their allies, but vowed to keep hitting them with targeted bombing when necessary.
"Saudi Arabia's renewed bombing campaign in Yemen sent crude oil higher, with Brent rising to new 2015 highs," added CMC Markets analyst Jasper Lawler.
After the end of Operation Decisive Storm, the coalition said the campaign would enter a second phase called Operation Renewal of Hope focusing on resuming political talks, aid deliveries and "fighting terrorism".