Asian equity markets broadly advanced early Thursday, buoyed by signs of cooling U.S. inflation that tempered expectations for a Federal Reserve rate increase, while oil prices retreated on a surprise build in U.S. inventories.

Data released Wednesday showed the inflation rate eased to 3.4% in July from 3.5% in June.

"Softer U.S. inflation, both in the headline and core, provides comfort that inflation is not re-accelerating dangerously, although pipeline risks from energy and chip-flation remain," Vishnu Varathan, head of APAC macro strategy at Mizuho Securities, said in a note

South Korea's Kospi index led the regional advance, rising 4.1%. The Shanghai Composite Index was up 0.4%, and Japan's Nikkei Stock Average added 1.6%, while Hong Kong's Hang Seng Index fell 0.2%.

Meanwhile, oil prices declined after data from the U.S. Energy Information Administration showed Wednesday that crude oil inventories rose unexpectedly last week, driven by an increase in imports and a decline in exports. Commercial crude oil stocks, excluding the Strategic Petroleum Reserve, rose by 17.4 million barrels to 424.4 million barrels in the week ended Aug. 7 and were about 2% below the five-year average for the time of year, the EIA said.

Oil prices were also weighed down by the Organization of the Petroleum Exporting Countries lowering its forecast for global oil-demand growth this year amid stalled talks to reopen the critical Strait of Hormuz and ongoing risks in the Red Sea, which continue to disrupt global supply chains.

President Trump said Wednesday that the U.S. has total control of the Strait of Hormuz but few ships are moving through the waterway given the risk of Iranian attacks. Ship-tracking data showed that just 14 vessels on Tuesday crossed a waterway that routinely handled more than 130 a day before the war.

"Ongoing deadlock in Middle East peace negotiations and Iran's increasingly assertive military posture kept geopolitical risk elevated, partially offsetting the constructive inflation print," OCBC Global Research said in a note.

Front-month West Texas Intermediate crude oil futures were down 1.3% to $82.22 a barrel, while front-month Brent crude oil futures slipped 1.1% to $87.98 a barrel, according to ICE data.