US benchmark West Texas Intermediate was trading 35 cents higher at $44.64 and Brent crude was up 38 cents at $47.80 a barrel at around 0245 GMT.
A bullish US jobs market report last week sent the dollar higher, which would make dollar-priced oil more expensive for holders of weaker currencies, hurting demand and prices.
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"That led to strong gains of the dollar on expectations for an increase in the interest rate by the Federal Reserve in their next meeting scheduled in December," said Sanjeev Gupta, head of the Asia Pacific oil and gas practice at professional services firm EY.
A hike in interest rates encourages investors back to US assets for higher returns, pushing the dollar higher.
Data showing that crude imports from China, the world's second-biggest oil consumer, fell to the lowest level in five months is also helping keep a lid on prices in the face of a world supply glut.
China's crude imports fell to about 6.23 million barrels a day in October, Bloomberg News reported quoting data from the Beijing-based General Administration of Customs.
"With few signs of change in the short-term supply and demand fundamentals, crude oil prices are likely to remain range-bound in the coming weeks," Gupta said.
Oil prices have fallen by more than half since reaching peaks of over $100 a barrel in June last year due to an oversupply of the commodity and weak demand.
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