By Shariq Khan

BENGALURU (Reuters) - U.S. crude oil gained about 3% on Wednesday, narrowing the price gap with global benchmark Brent in a post-holiday response to supply cuts announced on Monday by Saudi Arabia and Russia.

U.S. West Texas Intermediate crude (WTI) rose $2 from Monday's close, or 2.9%, to settle at $71.79 a barrel. Brent crude futures rose 40 cents, or 0.5%, to settle at $76.65 a barrel, after gaining $1.60 a barrel on Tuesday.

There was no WTI settlement on Tuesday because of the U.S. holiday, so trade on Wednesday had it catching up with Brent's gains the previous day. Both benchmarks hit their highest level in nearly two weeks during Wednesday's session.

Saudi Arabia, the world's biggest crude exporter, on Monday said it would extend its voluntary output cut of 1 million barrels per day (bpd) to August. Russia and Algeria, meanwhile, are lowering their August output and export levels by 500,000 bpd and 20,000 bpd respectively.

Russia-Saudi oil cooperation is still going strong as part of the OPEC+ alliance, which will do "whatever necessary" to support the market, Saudi energy minister Prince Abdulaziz bin Salman said on Wednesday.

"The July voluntary cuts and the extension into August should considerably tighten the oil market, but investors will stay on the sidelines until oil inventories will show substantial draws," said UBS analyst Giovanni Staunovo.

U.S. crude stocks fell by about 4.4 million barrels last week, while gasoline and distillate inventories rose, according to market sources citing American Petroleum Institute figures.

Oil prices were largely unchanged following the API data, which was released after Wednesday's settlement. Government data on U.S. inventories is due at 11:00 a.m. EDT (1500 GMT) on Thursday.

The Fourth of July marks peak U.S. travel season and this week's inventories reports could play a big role in pushing oil prices higher or lower, traders said.

"I guess that limits the price move. It seems investors are in a 'I believe when I see' world," Staunovo said.

Morgan Stanley lowered its oil price forecasts, predicting a market surplus in the first half of 2024 with non-OPEC supply growing faster than demand next year.

Recent surveys have shown a slump in global factory activity, reflecting sluggish demand in China and Europe.

Market attention is also focused on interest rates, with U.S. and European central banks expected to increase rates further to tame stubbornly high inflation.

(Reporting by Shariq Khan; Additional reporting by Natalie Grover, Yuka Obayashi and Muyu Xu; Editing by Marguerita Choy, David Gregorio and Nick Zieminski)