US benchmark West Texas Intermediate (WTI) for July delivery gained 79 cents to $60.93 in Asia, while Brent crude for July was up 61 cents to $65.49 in mid-morning trade.
That came the day after strong gains that saw WTI jump $2 while Brent closed up $2.19.
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"A big drop in API inventories provided some justification for today's big move upward," said Nicholas Teo, market analyst at CMC Markets in Singapore.
A dip in US stockpiles is seen as signalling healthy demand in the world's top crude consumer, supporting global prices.
Dealers expect that a drawdown of the United States' burgeoning reserves during the summer months, coupled with a slowdown in its shale output, could whittle down excess global supplies.
A surplus of US stocks was a key reason oil prices collapsed by more than 50% between June and January.
"We believe that only (if) US production starts to ease off, then we would be seeing improvements to the supply situation," said Daniel Ang, investment analyst at Phillip Futures in Singapore.
The Department of Energy's (DoE) petroleum report last week showed US output rose 20,000 barrels a day to 9.59 million in the week to May 29 -- the second consecutive gain and the highest since January 1983.
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