Benchmark Brent crude was up 4 cents or 0.1 per cent at $34.85 a barrel by 1205 GMT
Oil prices steadied amid signs that producers are cutting output, while traders waited for more clarity on demand as some countries gradually ease out of coronavirus lockdowns.
Benchmark Brent crude was up 4 cents or 0.1 per cent at $34.85 a barrel by 1205 GMT on Tuesday.
The front-month contract for US West Texas Intermediate crude was up 57 cents, or 1.8 per cent at $32.39 a barrel. The July contract, which was trading at vastly higher volumes, was up seven cents at $31.72 a barrel.
Global demand recovery is expected to be slow as some Covid-19 restrictions remain and there is a significant risk of repeat outbreaks and lockdowns.
There was little sign of a repeat of the historic plunge below zero seen last month amid signs of rising demand for crude and fuels.
The market was boosted earlier by signs that output cuts agreed by the Organisation of the Petroleum Exporting Countries and others including Russia (OPEC+), are being implemented.
OPEC+ cut its oil exports sharply in the first half of May, companies that track shipments said, suggesting a strong start in complying with their latest pact to curb output.
US production is also falling, with crude output from seven major shale formations expected to fall to 7.822 million barrels per day in June, the lowest since August 2018, according to the US Energy Information Administration.
A recovery in fuel demand in India also bought momentum in the first half of May.
For more news go to currency.com