Brent rose 12 cents, or 0.2pc, to $75.31 a barrel by 12:28 p.m. EDT (1628 GMT), after earlier rising to $75.78. U.S. crude slipped 1 cent to $73.07 a barrel, after hitting a session high of $73.61 earlier.
Brent crude rose 87 cents, or 1.2%, to $75.68 by 12:06 p.m. ET (1606 GMT). Its session high, $76.02 after the EIA data, was the highest since October 2018.
OPEC+ is discussing a gradual increase to oil output from August, but no decision has been taken on the exact volumes, an OPEC+ source said on Tuesday.
"Oil markets are rallying because OPEC is sceptical that the increase in U.S. oil production is going to be enough to change their plans to support prices," said Phil Flynn, senior analyst at Price Futures Group in Chicago.
Brent crude futures were down 86 cents, or 1.2%, at $72.22 a barrel.
The bullish trend in oil remains intact, thanks to optimism surrounding the demand outlook. The dollar may well be strengthening but the fundamental picture for oil hasn't changed.
Brent crude futures were down 52 cents, or 0.7%, at $72.56 a barrel.
US West Texas Intermediate (WTI) crude futures were down 39 cents, or 0.6%, at $70.65 a barrel, after retreating 1.5% on Thursday and is also set to be flat on the week.
Even the return of Iranian exports if the United States rejoins a nuclear agreement and lifts sanctions on Tehran was unlikely to change the bullish picture, he said.