(Reuters) - Oil rose more than 3 percent on Thursday, pushing Brent crude to a 2015 high above $63 per barrel on increasing evidence that U.S. production is peaking, balancing a market that has been in heavy oversupply for more than a year.

Oil prices collapsed in the six months to January, pushing Brent down more than 60 percent to almost $45 a barrel.

But the market has gradually recovered this year as much lower prices have discouraged oil exploration and production, especially in the United States.

"People are realizing that the U.S. production juggernaut is slowing, at least for now," said Virendra Chauhan, oil analyst at London-based consultancy Energy Aspects.

"U.S. production is down for the second time in three weeks and refinery runs are spiking up, driving demand higher."

Brent crude futures for June on Thursday hit $63.29 a barrel, the highest since December, after the previous much weaker front-month futures contract, for May, expired on Wednesday.

By 0835 GMT, June Brent was at $62.52 a barrel, down 80 cents from the previous close for June, but up sharply from Wednesday's close for May at $60.32.

U.S. crude was at $56.00, down 39 cents after hitting a 2015 high of $56.69 on Wednesday.

U.S. crude has been logging its strongest upswing this year as ebbing fears of an inventory overflow and renewed hedging in far-distance futures flatten the forward curve.

"We turn extremely bullish on oil," Singapore-based energy brokerage Phillips Futures said in a note to clients.

"This whole rally was primarily due to drops in U.S. crude production. We see the four-week average for crude production turning negative for the first time since July '14," it added.

Reuters technical analyst Wang Tao told Reuters Global Oil Forum that Brent could rise towards $70 a barrel in the near term, but that a sharp downturn could happen after that.

U.S. oil prices jumped on Wednesday after U.S. inventories built up more slowly than expected, although still to a new record. Talks between major oil producers also triggered speculation of production cuts, even though most analysts said these were unlikely.

Despite the oil price rally, the market remains oversupplied, analysts say.

"The recent bounce comes despite a surge in OPEC crude oil production in March which is likely to have been sustained in April," ANZ bank said.