However, some of those gains were chipped away last week as talk of a possible US interest rate hike lifted the dollar -- making oil more expensive -- and a report showed another jump in US crude stockpiles.
At around 0355 GMT, US benchmark West Texas Intermediate rose 31 cents, or 0.79%, to $39.77. Brent was up 28 cents, or 0.69%, at $40.72.
Members of the Organization of the Petroleum Exporting Countries (OPEC) and key non-members led by Russia are due to discuss a proposed output freeze at a meeting in Doha on April 17.
Bernard Aw at IG Markets
said a dip in the number of oil rigs in operation provided some buying incentives, although business has been slim owing to the long Easter break across most world markets.
However, he warned that "the fundamental picture of oil is still a little bit bearish" owing to a global supply glut and a slowdown in the global economy, particularly China.
He added, "Everything hinges on the meeting between OPEC and non-OPEC producers. If it takes place and they come to some agreement of a production freeze, we could see some gains well beyond $40."
Qatar's energy minister Mohammed al-Sada, who also serves as OPEC president, earlier said the initiative is backed by 15 countries accounting for about 73% of worldwide output.
Sanjeev Gupta, who heads the Asia-Pacific oil and gas practice at professional services firm EY, said traders will also be looking at upcoming US and Chinese data for direction.
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