* Funding impasse brings government to brink of shutdown
* EIA may not publish weekly oil data
* Easing Iranian tensions weigh on oil prices (New throughout, adds new quotes. Updates to settlement prices.)
NEW YORK, Sept 30 (Reuters) - Crude oil on both sides of the Atlantic fell on Monday but pared losses late in the day as traders bought contracts to square short positions as the third quarter ended and as the likelihood of an imminent U.S. government shutdown remained uncertain.
The Democratic-led Senate and the Republican-led House of Representatives could not come to terms on an agreement to end a stalemate on how to fund the U.S. government beyond Monday.
Senate Democrats shot down a proposal by the Republican-led House of Representatives to delay President Barack Obama's health care program for a year in return for temporary funding.
A senior House Republican said he did not think federal government agencies would shut down at midnight, but he did not provide details on how that might be avoided.
"I think there's still a lot of uncertainty with regard to the shutdown with the government," said Stephen Schork, editor of The Schork Report in Villanova, Pennsylvania. "You have some shorts looking to get out, looking to get some money off the table."
A government shutdown was expected to cut into demand in the world's largest oil consumer, weighing on prices. It would force hundreds of thousands of U.S. government employees across the country to stay home without pay.
The U.S. Energy Information Administration said it does not yet know if it will be able publish its weekly inventory data in the event of a shutdown.
U.S. crude settled 54 cents lower at $102.33 a barrel, paring losses from a session low of $101.05. Front-month U.S. crude oil futures ended the month 4.6 percent lower, the first monthly loss since May.
U.S. crude oil futures ended the third quarter 6.3 percent higher as tensions in the Middle East drove prices to a more than two-year high in August.
Front-month Brent crude oil futures settled 26 cents lower at $108.37 a barrel, losing 5.1 percent for the month, also the first monthly decline since May.
Brent hit a session low of $107.22 but ended the quarter with a 5.8 percent increase, also driven by sharp gains in August.
U.S. gasoline futures led the complex down earlier in the day as traders sold positions as the front-month contract expired at the end of trading on Monday. The October contract expired 1.5 percent lower at $2.63 per gallon.
"The amount of gasoline we have on hand is more than ample," said Gene McGillian, analyst at Tradition Energy in Stamford, Connecticut. "If we start to see refiners' seasonal maintenance programs pick up that may change."
Oil futures prices were also driven lower as tensions over Iran's nuclear program continued to ease.
Obama and new Iranian President Hassan Rouhani spoke by telephone on Friday, the highest-level contact between the two countries in three decades as the two sides seek a deal over Iran's nuclear program.
Exports from Iran have more than halved in recent years to around 1 million barrels per day in 2012 due to tightening sanctions.
Still, even with signs of rapprochement, the earliest that Iranian oil would come on the market is six to 12 months, said Ed Morse, managing director of commodity research at Citigroup in New York.
"On the best time frame on an agreement, oil will remain off the market in substantial volumes for six months, if not 12 months," Morse said, noting that a deal would have to be reached on restricting uranium enrichment with the West, and the United States would have to ease laws that make allowing increased exports difficult.
World powers are due to hold a new round of talks over Iran's nuclear program in mid-October in Geneva.
Supply concerns have also eased in recent weeks as exports from Libya have recovered to above 580,000 barrels per day, following weeks of disruption.
Investors cut their net long positions in Brent for a fourth week in a row to 167,745 contracts, the Intercontinental Exchange said. (Additional reporting by Matthew Robinson and Anna Sussman in New York, Ron Bousso in London, Florence Tan in Singapore; Editing by Jane Baird, Keiron Henderson, John Wallace and Peter Galloway)