After gaining over 5% in the prior two sessions, Brent futures rose 19 cents, or 0.3%, to settle at $68.65 a barrel, while U.S. West Texas Intermediate (WTI) crude rose 2 cents to settle at $66.07, Reuters reported. 

That was the highest close for both benchmarks in a week.

In post-settlement trade, Brent crude pared gains slightly and U.S. crude fell to $65.99 after trade group the American Petroleum Institute released weekly inventory estimates.

U.S. crude oil and fuel inventories fell last week, according to two market sources, citing American Petroleum Institute figures on Tuesday. Crude stocks fell by 439,000 barrels in the week ended May 21, the data showed, according to the sources, who spoke on condition of anonymity. API did not respond to a request for comment.

During the session, crude prices were supported by the decline in the U.S. dollar (.DXY) to a 19-week low versus a basket of currencies as inflation worries recede. A weaker dollar makes it less expensive for holders of other currencies to buy commodities priced in dollars, like oil.