The price of oil rose fell toward $95 a barrel Thursday, dragged down by evidence the U.S. crude supplies are growing.

Benchmark oil for July delivery fell 62 cents to $95.26 per barrel at late afternoon Bangkok time in electronic trading on the New York Mercantile Exchange. The contract rose 50 cents to close at $95.88 a barrel on the Nymex on Wednesday.

Ample supplies worked to press down prices. The American Petroleum Institute released data on crude inventories for the week ending June 7 that showed an increase of 794,000 barrels to 386.3 million barrels.

That compares to data released Wednesday by the U.S. Energy Department, which reported that oil supplies rose last week by 2.5 million barrels, or 0.6 percent, to 393.8 million barrels, which is 2.4 percent above year-ago levels.

Given the weak demand outlook U.S. inventories unsurprisingly came in above expectations with a build of 2.5 million barrels, said Michael Hewson of CMC Markets. Markets had been expecting a decline of 1.4 million barrels, he said in an email commentary.

On Wednesday, the International Energy Agency cut its forecast for global crude demand in 2013 by 80,000 barrels a day. It now expects the world to consume 90.6 million barrels a day this year, 785,000 barrels a day more than in 2012.

Brent crude, a benchmark for many international oil varieties, fell 61 cents to $102.96 a barrel on the ICE Futures exchange in London.

In other energy futures trading on the Nymex:

— Wholesale gasoline fell 0.7 cent at $2.8027 a gallon.

— Heating oil fell 1.9 cents to $2.8756 per gallon.

— Natural gas fell 2.4 cents to $3.753 per 1,000 cubic feet.