Brent crude gained $1.79, or 2.1%, to $87.40 a barrel by 1 p.m. EDT (1700 GMT) while U.S. West Texas Intermediate rose $1.92, or 2.3%, to $83.43. Prices had risen about 2% on Tuesday, Reuters reported.

The U.S. Consumer Price Index (CPI) climbed 0.1% last month after advancing 0.4% in February, the Labor Department said. In the 12 months to March 31 the CPI increased 5%, the smallest year-on-year gain since May 2021. The CPI rose 6% year on year in February.

"The CPI number implies, to a certain degree, that the Fed will start cutting rates by the end of the year. That's a positive demand development for energy," said Robert Yawger, director of energy futures at Mizuho Securities.

Government bonds, a gauge of global stocks, and gold rallied while the dollar dropped sharply after the data. A weaker U.S. currency also makes dollar-priced oil cheaper for buyers holding other currencies.

Hedge fund were buying oil futures in the market over the past few days, in anticipation of improving demand, said Dennis Kissler, senior vice president of trading at BOK Financial.

U.S. President Joe Biden's top economic adviser and ex-Federal Reserve vice chair, Lael Brainard, also said she was seeing inflation coming down.

Markets shrugged off a small build in U.S. crude oil stocks, attributing it in part to a congressionally mandated release of oil from the U.S. emergency reserve and lower exports at the start of the month.

Crude inventories (USOILC=ECI) rose by 597,000 barrels in the last week to 470.5 million, compared with analysts' expectations in a Reuters poll for a 600,000 barrel drop.

U.S. gasoline stocks (USOILG=ECI) fell by 300,000 barrels, while distillate stockpiles (USOILD=ECI), which include diesel and heating oil, fell by 0.6 million barrels. Both drawdowns were smaller than analysts' forecasts.

Meanwhile, a report from the American Petroleum Institute (API) showed crude inventories rose by about 380,000 barrels in the last week, while gasoline inventories were also higher, according to sources.

In a negative for oil demand, the International Monetary Fund on Tuesday trimmed its 2023 global growth outlook, citing the impact of higher interest rates.

The market is also waiting for clarity on oil demand and supply, with monthly reports from the Organization of the Petroleum Exporting Countries (OPEC) and the International Energy Agency due on Thursday and Friday, respectively.

The U.S. Energy Information Administration on Tuesday cut its forecast for oil production by OPEC countries by 0.5 million barrels per day for the rest of 2023 and cut its 2023 world oil demand growth forecast by 40,000 bpd.