Brent futures had edged up 20 cents to $79.60 a barrel by 1145 GMT, while U.S. West Texas Intermediate (WTI) crude rose 30 cents to $75.13 a barrel, Reuters reported.

"Fundamentally, we should reach a supply deficit situation in the third quarter, but whether that is trumped by recession concerns and cautious sentiment around rate hikes remains to be seen," DBS Bank's lead energy analyst Suvro Sarkar said.

U.S. inflation data later on Wednesday will provide clues on the interest rate outlook in the world's biggest economy.

Markets expect one more rise, but that the U.S. rate-hiking cycle is peaking. Higher rates can slow economic growth and reduce oil demand.

U.S. crude inventories rose about 3 million barrels in the week to July 7, market sources said, citing American Petroleum Institute industry figures. Analysts polled by Reuters expected a 500,000-barrel rise in crude stocks.

Nevertheless, forecasts from the U.S. Energy Information Administration (EIA) and the International Energy Agency (IEA) point to the market tightening into 2024.

Meanwhile, The IEA expects the oil market should stay tight in the second half of 2023, citing strong demand from China and developing countries combined with supply cuts from leading producers. New forecasts from the IEA are expected this week.

"The oil balance gets tighter either when supply is downgraded, or demand is revised up. If both happens at the same time the change can be seismic," said PVM analyst Tamas Varga referring to the EIA's outlook.

"Clearly, it is not worried about inflation-induced recession that could potentially dent global oil consumption."

Oil prices are also being supported by a weaker dollar and optimism surrounding Chinese stimulus, noted Fiona Cincotta, senior financial markets analyst at City Index.

Top producer Saudi Arabia pledged last week to extend a production cut of 1 million bpd in August, while Russia will cut exports by 500,000 bpd.