* U.S. asks some OPEC members to pump more oil sources
* Market focuses on oil supplies, OPEC meeting on June 22
* POLL-U.S. crude oil inventories seen down last week
* Coming Up: API U.S. oil data at 4:30 p.m./2030 GMT (Updates to market settle, adds commentary)
NEW YORK, June 5 (Reuters) - Brent crude reversed losses on Tuesday, after hitting its lowest price in nearly a month following a report that the U.S. government asked Saudi Arabia and other major exporters to increase oil output.
Brent crude futures rose 9 cents to settle at $75.38 a barrel, a 0.12 percent gain. It touched a low of $73.81, its lowest since May 8.
U.S. West Texas Intermediate (WTI) crude futures rose 77 cents to settle at $65.52 a barrel, a 1.2 percent gain. Earlier, WTI hit a session low of $64.22, the lowest since April 10.
The premium for Brent to WTI hit a session low of $9.38, recovering slightly from last week when the spread reached $11.57, the widest since March 2015. That divergence was "overcooked," prompting profit-taking, said Jim Ritterbusch, president of Ritterbusch and Associates.
The U.S. government has unofficially asked Saudi Arabia and some other OPEC producers to raise oil output, three OPEC and industry sources said, although it has not requested a specific figure.
Earlier on Tuesday, Bloomberg reported that the U.S. government had asked the producers to increase oil production by about 1 million barrels per day (bpd).
OPEC supply tends to more directly influence Brent, whereas U.S. crude futures are tied to U.S. supply.
The request comes after U.S. retail gasoline prices surged to their highest in more than three years and President Donald Trump in April complained about OPEC policy and rising oil prices. The national average on Tuesday was $2.94 a regular gallon, according to AAA.
It also follows Washington's decision to reimpose sanctions on Iran's crude exports, which could disrupt global oil supply. Iran's crude oil output could fall 1 million bpd as a result of renewed U.S. sanctions, according to a note from Standard Chartered.
"Markets are forward-looking. The fact that Russia, Saudi Arabia and OPEC more broadly have started discussing raising output levels, you've got this pretty swift correction," said Tyler Richey, co-editor of the Sevens Report in Jupiter, Florida.
Saudi Arabia and Russia were already discussing raising OPEC and non-OPEC oil output by around 1 million bpd, sources familiar with the matter said on May 25.
Saudi Aramco has raised its July price for its Arab Light grade for Asian customers by 20 cents a barrel versus June to a premium of $2.10 a barrel to the Oman/Dubai average, it said on Tuesday.
The Organization of the Petroleum Exporting Countries meets in Vienna on June 22 to decide whether the group and non-OPEC producers, including Russia, should raise output to make up for any supply shortfall from Iran and Venezuela.
U.S. crude oil stockpiles were forecast to have fallen for the second consecutive week, a preliminary Reuters poll showed on Monday.
Industry group American Petroleum Institute (API) is scheduled to release its data for last week at 4:30 p.m. EDT (2030 GMT) on Tuesday, and government figures are due at 10:30 a.m. EDT (1430 GMT) on Wednesday. (Additional reporting by Amanda Cooper in London, Jane Chung in Seoul and Roslan Khasawneh in Singapore; Editing by Marguerita Choy and Edmund Blair)