New York's main contract, light sweet crude for March delivery, gained eight cents to 34.70 dollars a barrel, within sight of the 32.40 dollars hit on December 18, when prices touched their lowest point in nearly five years.
Brent North Sea crude for April delivery was 39 cents higher at 39.94 dollars.
Sentiment remained weak, with investors still concerned about the state of the US economy, the world's biggest energy user, dealers said.
The US Federal Reserve in its latest forecast Wednesday said the US economy would shrink this year by 0.5 to 1.3 percent while unemployment is forecast to rise from 8.5 to 8.8 percent.
Author: Ksenia Kochneva
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Oil Prices Higher in Asia
Oil prices were higher in Asian trade Thursday ahead of a report expected to show a build-up in US crude inventories during the recession, dealers said