May 31 (Reuters) - Oil prices settled lower on Wednesday, pressured by a stronger U.S. dollar and weak data from top oil importer China that fed demand fears.

Brent crude futures for August delivery settled down $1.11 to $72.60 a barrel. U.S. West Texas Intermediate crude (WTI) settled down $1.37, or 2%, to $68.09.

At their session lows, both benchmarks were down more than $2 to multi-week lows. On Tuesday, both fell more than 4%.

Oil prices tumbled after Chinese data showed manufacturing activity contracted faster than expected in May, as weakening demand cut the official manufacturing purchasing managers' index (PMI) down to 48.8 from 49.2 in April, lagging a forecast of 49.4.

The dollar index, which measures the U.S. unit against six major peers, saw support from cooling European inflation and progress on a bipartisan U.S. debt ceiling bill, which will advance to the House of Representatives for debate.

House passage would send the bill to the Senate, where debate could stretch to the weekend, as a June 5 deadline loomed.

A stronger dollar makes oil more expensive for buyers holding other currencies.

U.S. data showed job openings unexpectedly rose in April, pointing to persistent strength in the labor market that could push the Federal Reserve to raise interest rates in June.

"We have weaker-than-expected Chinese data, the debt limit situation, two years of flat spending, and likely another rate hike next month weighing on markets," said Bob Yawger, director of energy futures at Mizuho.

Traders will watch the upcoming June 4 meeting of OPEC+ - the Organization of the Petroleum Exporting Countries and allies including Russia. Mixed signals by major producers on further production cuts have sparked volatility in oil prices, yet banks HSBC and Goldman Sachs and analysts do not expect OPEC+ to announce further cuts at this meeting.

HSBC said stronger oil demand from China and the West from the summer onwards will trigger a supply deficit in the second half.

"The most likely action is inaction," said PVM oil market analyst Stephen Brennock, regarding the OPEC+ decision.

In the U.S., field production of crude oil rose in March to 12.696 million barrels per day, the highest since March 2020, when the coronavirus pandemic began to decimate global energy demand, Energy Information Administration data showed.

U.S. crude oil and gasoline stockpiles were seen falling last week, while distillate inventories likely increased, a preliminary Reuters poll showed on Tuesday.

The poll was conducted ahead of reports from the American Petroleum Institute, an industry group, due at 4:30 p.m. EDT (2030 GMT) on Wednesday. (Additional reporting by Rowena Edwards in London, by Trixie Yap in Singapore, Stephanie Kelly in New York, and Yuka Obayashi in Tokyo Editing by David Evans, Emelia Sithole-Matarise, Lisa Shumaker and David Gregorio)