At around 1230 GMT, the US benchmark West Texas Intermediate (WTI) for delivery in April climbed 52 cents to stand at USD 34.27 a barrel.
In London, Brent North Sea crude for May advanced 29 cents to USD 36.86 a barrel compared with Monday's close.
Sentiment was boosted further by China's decision yesterday to slash the so-called reserve requirement ratio (RRR) for banks, freeing up additional funds for lending.
The move stoked expectations for stronger demand in the world's largest energy consumer.
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"In principle, the cut in RRR should encourage lending, support the economy and therefore oil demand. At the same time, production seems to be slipping in the United States, Mexico and even in OPEC."
Prices had also risen yesterday as oil kingpin Saudi Arabia suggested it was open to a coordinated solution to market volatility while insisting it would not cut production.
The oil market has slumped by 70 per cent since mid-2014 on oversupply concerns at a time when global economic growth is faltering.