* Libya output at 210,000 bpd; western oilfields shut
* Total, Sonatrach cut Libyan staff
* U.S. crude stocks seen up 800,000 barrels last week -poll
* Crude stocks fall by 10.3 million barrels - API (Adds API data)
NEW YORK, May 20 (Reuters) - Brent rose modestly on Tuesday supported by instability in Libya, pulling U.S. oil for July delivery higher in spite of expectations for an increase in domestic stockpiles.
The El Feel and El Shahara oilfields in western Libya were still shut more than a week after the government said protests there were over, an official said, and output was flat at 210,000 barrels a day.
Violence among rival militias and an attack on parliament on Sunday by armed men claiming loyalty to retired Major General Khalifa Haftar led French oil major Total SA to cut its presence in Tripoli and Algerian state energy company Sonatrach began evacuating workers.
The movement by Haftar may signal an attempt to draw up a broader anti-Islamist front that risks a wider battle in the North African state, which is trying to boost oil exports crucial to the economy.
U.S. commercial crude stockpiles likely surged to their highest in more than 20 years, a Reuters poll found.
Brent crude settled 32 cents higher at $109.69 a barrel. U.S. crude for June delivery, which expired Tuesday, settled 17 cents lower at $102.44, after hitting its highest price in nearly one month on Monday. U.S. crude for July delivery settled 22 cents up at $102.33 a barrel.
"I think we are worried about Libya, but it seems that the market wasn't ever convinced it would be a reliable supplier and that's why you're not seeing any major follow through moves higher after the initial spike up on Monday," said Phil Flynn, analyst at Price Futures Group in Chicago.
RECORD-HIGH U.S. STOCKS
A Reuters poll found U.S. commercial crude stocks were expected be up by 800,000 barrels in the week to May 16, while gasoline stocks likely rose 100,000 barrels and refinery runs were up 0.6 percent.
U.S. crude stocks rose in the week to May 9, with inventories rising 947,000 barrels as production hit a 28-year high of 8.43 million barrels per day, according to data from the EIA.
A report released after the settlement by the industry group the American Petroleum Institute showed an unexpected drop in crude stocks of 10.3 million barrels. The report lent support to U.S. crude futures for July, which extended gains in post-settlement trading.
The more closely watched EIA data will come out Wednesday at 10:30 a.m. EDT (1430 GMT).
This weekend marks the start of the U.S. summer driving season with Monday's Memorial Day holiday.
Ukraine is set to hold presidential elections Sunday. A senior Russian official said the vote risks deepening divisions absent any "road map" to end the crisis. (Additional reporting by Elizabeth Dilts in New York, Lin Noueihed in London and Jacob Gronholt-Pedersen in Singapore; Editing by David Evans, Jane Baird, James Dalgleish and Andre Grenon)