Brent crude was up 55 cents, or 0.8%, to $67.66 a barrel at 1301 GMT, while U.S. West Texas Intermediate crude rose 58 cents, or nearly 0.9%, to $66.03 a barrel.
Brent has traded between a high of $69.05 a barrel and low of $66.34 since June 25, as concerns of supply disruptions in the Middle East have ebbed following a ceasefire between Iran and Israel.
Iran enacted a law on Wednesday that stipulates any future inspection of its nuclear sites by the International Atomic Energy Agency needs approval by Tehran s Supreme National Security Council. The country has accused the agency of siding with Western countries and providing a justification for Israel s air strikes.
"The market is pricing in some geopolitical risk premium from Iran s move on the IAEA," said Giovanni Staunovo, a commodity analyst at UBS. "But this is about sentiment, there are no disruptions to oil."
Planned supply increases by the Organization of the Petroleum Exporting Countries and its allies including Russia, a group known as OPEC+, appear already priced in by investors and are unlikely to catch markets off-guard again imminently, said Priyanka Sachdeva, senior market analyst at brokerage Phillip Nova.
Four OPEC+ sources told Reuters last week the group plans to raise output by 411,000 barrels per day next month when it meets on July 6, a similar amount to the hikes agreed for May, June and July.
"We are all talking about additional supply coming to the market, but the supply has not really hit the market," UBS Staunovo said. "Probably because it s being consumed domestically."
Saudi Arabia lifted shipments in June by 450,000 bpd from May, according to data from Kpler, its biggest increase in more than a year. However, overall OPEC+ exports are relatively flat to slightly down since March, Staunovo said. He expects this trend to persist over the summer as hot weather drives higher energy demand.
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The greenback continued to weaken, falling to a 3-1/2-year low against its major peers on Wednesday. A weaker dollar tends to support oil prices, as it can boost demand for buyers paying in other currencies.
The release of the key U.S. monthly employment report on Thursday will shape expectations around the depth and timing of interest rate cuts by the Federal Reserve in the second half of this year, said Tony Sycamore, an analyst at IG.
Lower interest rates could spur economic activity, which would in turn boost oil demand.
Official U.S. oil stockpile data from the Energy Information Administration is due to be released at 10:30 a.m. EDT (1430 GMT) on Wednesday.
American Petroleum Institute data late on Tuesday showed U.S. crude oil inventories rose by 680,000 barrels in the past week at a time when stockpiles are typically drawn down amid summer demand, sources said.
