* OPEC, non-OPEC may ease cuts 'softly' - Novak
* OPEC set to meet next month to discuss policy
* Dollar falls after Trump scraps Kim summit, supportive for oil (Updates prices, market activity, adds commentary; changes byline, dateline, previous LONDON)
By Stephanie Kelly
NEW YORK, May 24 (Reuters) - Oil prices fell about 1 percent on Thursday, with expectations building that OPEC could wind down the output deal in place since the start of 2017, due to supply concerns out of Venezuela and Iran.
Brent crude futures fell 61 cents, or 0.8 percent, to $79.19 a barrel by 11:24 a.m. EDT (1524 GMT). U.S. West Texas Intermediate (WTI) crude futures fell 67 cents to $71.17 a barrel, a 0.9 percent loss.
The Organization of the Petroleum Exporting Countries may decide in June to lift output to make up for reduced supply from Venezuela and Iran, the latter in part due to the U.S. decision to withdraw from the Iran nuclear arms control deal, OPEC and oil industry sources told Reuters.
Russian Energy Minister Alexander Novak said production cuts could be eased "softly" if OPEC and non-OPEC countries see the oil market balancing in June, the Interfax news agency reported.
Russia and Saudi Arabia have a common position on the future of the oil output cut deal, Novak told Interfax news agency, though he said the deal would stay in place for now. Russia's Lukoil said the deal should remain in place but needs to be altered.
"A move to put more oil on the market by Saudi Arabia and Russia would be very bearish for prices. The mere contemplation of it has hit oil prices this week," said John Kilduff, a partner at Again Capital LLC in New York.
Venezuela's output has fallen to about 1.4 million barrels per day, according to OPEC secondary sources, as its economic crisis grows and state-run PDVSA struggles to pay its debts and fund operations.
Supply concerns have pushed Brent and WTI to multi-year highs, with Brent breaking through an $80 threshold last week for the first time since November 2014.
OPEC and some non-OPEC major oil producers, which are scheduled to meet in Vienna next month, previously agreed to curb their combined output by about 1.8 million bpd to boost oil prices and clear a supply glut.
Global inventories have been broadly falling, even as U.S. crude production remains strong. The United States in February produced 10.3 million bpd, a record.
On Thursday, U.S. President Donald Trump called off a planned summit with North Korean leader Kim Jong Un over that nation's nuclear aims.
Trump's comments should be negative for oil prices, but the comments pushed the dollar index down, supporting crude futures, Commerzbank strategist Carsten Fritsch said.
A weaker dollar makes greenback-denominated commodities less expensive for holders of other currencies. The dollar fell more than 0.2 percent against a basket of currencies. (Additional reporting by Amanda Cooper and Ahmad Ghaddar in London, Jane Chung in Seoul and Jessica Jaganathan in Singapore Editing by Marguerita Choy and Mark Potter)