* U.S. crude, gasoline inventories rise unexpectedly -EIA
* OPEC, non-OPEC may ease cuts 'softly' - Novak
* OPEC set to meet next month to discuss policy (Adds Novak comment, updates prices)
LONDON, May 24 (Reuters) - Oil prices recorded their largest one-day drop in two weeks on Thursday, with expectations building that OPEC could wind down an output deal that has been in place since the start of 2017 due to concerns about supplies from Venezuela and Iran.
Benchmark Brent futures were down $1.02 at $78.78 a barrel by 1353 GMT, the largest one-day fall since May 8, while U.S. crude futures dropped $1.08 to $70.76 a barrel.
"This discussion about possible OPEC supply increases after the June meeting has put a brake on the oil price for the time being, so $80 is a big hurdle to overcome," Commerzbank strategist Carsten Fritsch said.
"If prices get above there, that will further intensify and increase the likelihood that OPEC will do something ....It's going to be very difficult to overcome this level on a sustainable basis before the OPEC meeting."
The Organization of the Petroleum Exporting Countries may decide in June to lift output to make up for reduced supply from Iran and Venezuela and in response to concerns from Washington about a rally in oil prices, 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.
Venezuela's output has fallen amid an economic crisis, while Iran's supply is threatened by U.S. sanctions.
These factors have helped push 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 barrels per day (bpd) to boost oil prices and clear a supply glut.
Global inventories have been broadly falling. But commercial U.S. crude inventories rose
Inventories of gasoline rose by 1.9 million barrels in the same week, just ahead of the Memorial Day holiday in the United States which typically marks the start of the summer driving season.
Refinery runs fell 7,000 bpd to 16.63 million bpd, 3.8 percent below the same week last year, according to the EIA data. (Additional reporting by Ahmad Ghaddar in London, Jane Chung in Seoul and Jessica Jaganathan in Singapore Editing by Edmund Blair and Mark Potter)