TOKYO: Oil prices inched higher on Wednesday, extending the previous day's rally, after industry data showed U.S. crude stocks fell more than expected last week, though a bigger-than-anticipated build in products inventories capped gains.

Brent crude futures rose 29 cents, or 0.4%, to $77.88 a barrel at 0138 GMT, while U.S. West Texas Intermediate crude futures climbed 29 cents, or 0.4%, to $72.53 a barrel.

The benchmarks gained about 2% on Tuesday amid the Middle East crisis and a Libyan supply outage.

"We saw a correction yesterday, as the market had fallen too much earlier the week and as a drop in the U.S. crude inventories provided support," said Yuki Takashima, an economist at Nomura Securities.

"Investors' attention is back on a global supply and demand balance," he said, noting they are waiting for the U.S. Energy Information Administration's (EIA) weekly data due later today and a monthly report on oil demand and supply by the International Energy Agency (IEA) due next week.

U.S. crude oil inventories fell by 5.2 million barrels in the week that ended Jan. 5, according to market sources citing American Petroleum Institute figures on Tuesday, compared with analysts' estimates of 700,000 barrels increase in a Reuters poll.

However, gasoline inventories rose by 4.9 million barrels, while distillate inventories gained 6.9 million barrels, more than an estimated increase of 2.5 million barrels and 2.4 million barrels respectively.

The data of the EIA, the statistical arm of the U.S. Department of Energy, is due at 10:30 a.m. EST (1530 GMT) on Wednesday.

On the supply side, U.S. crude production will hit records over the next two years but grow at a slower rate, the EIA said on Tuesday, as efficiency gains offset a decline in rig activity.

In the Middle East, U.S. Secretary of State Antony Blinken urged Israel on Tuesday to make "hard choices" to normalise relations with more of its neighbours, a new appeal to smooth the path to creating a Palestinian state.

Investors are also looking for clues on when the Federal Reserve may begin cutting interest rates. Expectations the U.S. central bank could begin cutting rates as soon as March have decreased. (Reporting by Yuka Obayashi. Editing by Gerry Doyle)