"We turn extremely bullish on oil after yesterday's 5 percent rally in crude prices," Singapore-based energy brokerage Phillips Futures said.
"This whole rally was primarily due to drops in U.S. crude production. We see the 4-week average for crude production turning negative for the first time since July '14," it added.
Reuters technical analyst Wang Tao said in the Global Oil Forum that Brent could rise towards $70 a barrel in the near term, but that a sharp downturn could happen after that.
Read MoreThis chart says it's time to buy oil stocks: Analyst
Oil prices jumped on Wednesday after U.S. inventories built up more slowly than expected, though still to a new record, and talks between major oil producers this week triggered speculation of production cuts, even though most analysts said these were unlikely.
Crude prices have risen 15 percent since early April to their highest level since December last year, yet analysts said the market remained oversupplied, largely due to high production.
"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.
The International Energy Agency said on Wednesday that world oil markets may take longer to tighten than expected due to a surge in OPEC supply and a potential rise in Iranian exports, even as demand strengthens.
Energy consultancy Wood Mackenzie said the "low oil price leads to exploration budget cuts averaging 30 percent across the industry in 2015", but added that exploration cost deflation would average 33 percent, presenting an opportunity for strong explorers to increase drilling.