* Brent holds above $41, WTI stuck below $40
* Libya's talks to resume oil exports progress
* Coming Up: Weekly API stockpile data at 4:30 p.m./2030 GMT (New throughout, updates prices, market activity and comments to settlement)
By Laura Sanicola
NEW YORK, June 30 (Reuters) - Oil prices slipped on Tuesday as investors worried that rising COVID-19 cases would hurt demand while supply could rise with a potential resurgence of Libyan oil production, which has slowed to a trickle since the start of the year.
The more-active September contract for Brent LCOc2 settled down 58 cents at $41.27 a barrel. The August contract LCOc1 , which expires on Tuesday, fell 56 cents, or 1.2%, to $41.15. The contract has gained 16.5% this month so far, and 81% on the quarter.
U.S. crude CLc1 was down 43 cents, or 1%, at $39.27 a barrel. U.S. crude has risen 12.4% in the past month, up about 95% in the quarter, reflecting its recovery from late March. The contract pared losses in post-settlement trade after data from trade group the API showed a larger-than-expected draw in U.S. crude stockpiles.
Fuel demand has recovered from the worst weeks of the outbreak, but cases have been rising in southern and southwestern U.S. states. Northeastern states like New York and New Jersey doubled the number of states from which travelers face quarantine restrictions.
"Sustaining the independent show of gasoline strength will be challenged by coronavirus headlines where news has seen a definite negative shift in recent weeks," Jim Ritterbusch, president of Ritterbusch and Associates in Galena, Illinois, said in a report.
Investors will seek signs of demand recovery in weekly inventory data due on Tuesday from the American Petroleum Institute industry group and from the U.S. government on Wednesday. EIA/S
Libya is trying to resume exports, which have been almost entirely blocked since January due to civil war. The state's oil company hopes talks will end a blockade by eastern-based forces. we do finally see a resumption in Libyan output, this would make the job of OPEC+ a little bit more difficult," said Dutch bank ING.
A Reuters poll of analysts showed expectations that oil prices will consolidate at around $40 a barrel this year, with a recovery gaining steam in the fourth quarter.