By Sonali Paul

MELBOURNE  - Oil prices fell in early trade on Thursday after U.S. crude, gasoline and heating oil inventories all rose more than expected, dousing hopes of a smooth recovery in demand from coronavirus lockdowns.

The decline extended losses from Wednesday on uncertainty about Russia's commitment to deep oil production cuts in the lead-up to a June 9 meeting of the Organization of the Petroleum Exporting Countries and its allies, dubbed OPEC+.

U.S. West Texas Intermediate (WTI) crude futures fell as much as 5% to a low of $31.14 and were down 3%, or 97 cents, at $31.84 at 0019 GMT.

Brent crude futures last traded down 2.3%, or 78 cents, at $33.96.

Data from the American Petroleum Institute industry group showed crude stocks rose by 8.7 million barrels in the week to May 22, compared with analysts' expectations for a draw of 1.9 million barrels.

Gasoline stocks rose by 1.1 million barrels, more than 10 times the build analysts had expected, and stocks of diesel and heating oil rose by 6.9 million barrels, nearly four times as much as anticipated.

"It just indicates that demand recovery is progressing but it's not strong enough yet to be really self-sustaining," National Australia Bank's head of commodity research, Lachlan Shaw said.

The market will be looking to see if data from the U.S. Energy Information Administration later on Thursday matches API.

Shaw said crude was also weaker amid scepticism about the tightness of Russia's relationship with Saudi Arabia, even after Russian President Vladimir Putin and Saudi Crown Prince Mohammed bin Salman agreed on further "close coordination" on oil output cuts.

With WTI holding above $30, OPEC+ will be closely watching to see whether U.S. oil shale oil producers who have breakeven prices in the high $20 and low $30 dollar range step up production.

"There is a risk that we see those wells that have been shut in start to reverse and we see more supply return to the market," Shaw said.

(Reporting by Sonali Paul; editing by Richard Pullin)