West Texas Intermediate crude for April delivery, the main contract on the New York Mercantile Exchange, rose $3.44 a barrel from late Wednesday to close at $101.42.
In London, North Sea Brent jumped $4.28 to settle at $114.90.
"We haven't really seen any major change in the market dynamics that really explains today's price move," said Jason Schenker of Prestige Economics.
"But if you look across the board, we have generally a bounce-back on a number of markets from recent moves lower," he said.
He said traders had their eyes on the Middle East, where tensions continue in Bahrain, and the crisis at Japan's Fukushima nuclear plant.
"The chore now for oil market participants will be to parse how much significance to give to several competing influences," said Michael Fitzpatrick of the Kilduff Report.
The damage to Japan's economy, the world's third largest, should reduce demand there, Fitzpatrick said.
But at the same time, Bahrain's turmoil has drawn in Gulf rivals and oil giants Saudi Arabia and Iran, heightening tensions there.
And US economic data released Thursday suggests that economic activity in the world's biggest oil user is picking up speed.
"Weigh it all up (and) we will still have to give the nod to our short-term, across-the-board bullishness," Fitzpatrick said.
"But as events unfold in Japan or even in the Middle East, for that matter, reversals could come quickly."