* OPEC to meet in Vienna on June 22 to agree output policy
* Iran has so far resisted OPEC production rise
* Supply climb would come amid strong demand
* U.S. refinery runs hit record, crude stocks decline
* But Barclays warns of coming demand slowdown (Adds Rosneft production plans, updates prices)
By Henning Gloystein
SINGAPORE, June 21 (Reuters) - Oil prices fell on Thursday as Iran signalled it may support a small rise in OPEC crude output, possibly paving the way for the producer cartel to agree a supply increase during a meeting on Friday.
However, prices were prevented from dropping further by robust U.S. fuel demand seen in record refinery runs, strong travel data and a large decline in crude inventories.
Brent crude futures were at $74.34 per barrel at 0605 GMT, down 40 cents, or 0.5 percent, from their last close.
U.S. West Texas Intermediate (WTI) crude futures were at $65.50 a barrel, down 21 cents, or 0.3 percent.
Iran, a major supplier within the producer cartel of the Organization of the Petroleum Exporting Countries (OPEC), signalled on Wednesday it could agree on a small increase in the group's output during a meeting to be held at OPEC's headquarters in Vienna on June 22 together with non-OPEC member but top producer Russia.
"There appears to be an air of confidence that this deal will move through," said Stephen Innes, head of trading for Asia-Pacific at futures brokerage OANDA in Singapore.
"We expect OPEC and Russia to gradually add supplies back to the market by next year, mostly offsetting the almost 1 million barrels per day (bpd) supply disruption in Venezuela," Barclays bank said.
Tehran had previously resisted pressure by OPEC's de-facto leader Saudi Arabia to raise output.
Even with Iran appearing to fall in line, analysts do not expect a harmonious OPEC meeting.
"Our expectations are for a tense, discordant and highly geopolitical OPEC+ meeting," said Japan's Mitsubishi UFJ Financial Group in a note to clients.
OPEC, together with other key producers including Russia, started withholding output in 2017 to prop up prices, but a tightening market in 2018 led to calls by major consumers for more supplies.
Russia's Rosneft, the world's top listed oil producer by output, said it plans an ambitious 87 million tonnes of oil equivalent production expansion by 2022, to an overall output of 330 million tonnes in order to gain global market share.
In a sign of strong demand, U.S. refineries processed a seasonal record of 17.7 million bpd of crude oil last week, according to data from the Energy Information Administration (EIA) said on Wednesday.
This comes as a record 46.9 million Americans are expected to travel during the upcoming July 4 holiday, according to the American Automobile Association on Thursday, which is seen as a leading indicator for U.S. fuel demand.
Amid healthy consumption, commercial U.S. crude inventories dropped by 5.9 million barrels in the week to June 15, to 426.53 million barrels C-STK-T-EIA, the EIA said.
U.S. crude oil production C-OUT-T-EIA was flat week-on-week, remaining at a record 10.9 million bpd.
Beyond the short-term, Barclays said there were headwinds for oil prices.
"Deleveraging in China and a weakening in the narrative around synchronous global economic growth are likely to add headwinds for all commodities," it said.
Reporting by Henning Gloystein; Editing by Richard Pullin and Joseph Radford