LONDON, July 10 (Reuters) - A recent escalation of hostilities between the U.S. and Iran could upend the International Energy Agency's forecast of a significant oil market surplus next year, it said on Friday, as global supply jumped in June when the Strait of Hormuz reopened but still lagged pre-war levels.

Global oil markets received some respite last month as a peace agreement between the U.S. and Iran facilitated the opening of the Strait, the effective closure of which had taken out as much as 14 million barrels per day of crude flows during the peak of the largest oil supply crisis in history.

Global oil supply rose by 4.1 million bpd in June, the agency said, but remained 9.4 million bpd below pre-war levels. The agency predicts supply will expand by 7.5 million bpd next year, but this is contingent on improved Hormuz transits.

"An escalation in hostilities on 7-8 July, however, clouds the outlook and could upend the forecast that sees the market flipping to a surplus next year," it said.