Brent crude futures were up 46 cents, or 0.6%, to $78.15 a barrel by 0802 GMT, and U.S. West Texas Intermediate crude was up 48 cents, or 0.7%, at $73.47, Reuters reported.

Supply cuts by top exporters Saudi Arabia and Russia set for August helped to lift the benchmark prices, which were also supported as the U.S. dollar fell to a two-month low.

A weaker dollar makes crude cheaper for holders of other currencies and often boosts oil demand.

"Oil has found a floor and the only thing ... that could break that is if U.S. inflation is scorching hot and the Fed is forced to tighten this economy into a recession," said Edward Moya, an analyst at OANDA.

While central bank officials said the U.S. Federal Reserve will likely raise interest rates further to tame persistent inflation, markets are somewhat pacified by indications that the months of monetary policy tightening are nearing an end.

"Nevertheless, nerves are not completely calmed just yet. Anxiety is still palpable that recession fears could lead to downgrades in oil demand," said PVM analyst Tamas Varga.

Still, the International Energy Agency (IEA) is standing firm with the expectation that oil demand from China and developing countries, combined with recently announced supply cuts, is likely to keep the market tight in the second half of the year despite a sluggish global economy, its head said on Monday.

China's decision to boost support for its real estate sector bolstered the hope for an uptick in demand there, analysts said.