May 7 (Reuters) - Major Gulf stock markets climbed in early Thursday trading, supported by strong corporate earnings and optimism over a potential U.S.-Iran peace deal, though uncertainty persisted over the fate of the strategically vital Strait of Hormuz.

On Wednesday, Iran said it was reviewing a U.S. peace proposal which, according to sources, would officially bring the war to an end but would leave unresolved Washington's main demands that Tehran halt its nuclear program and reopen the Strait of Hormuz.

Saudi Arabia's benchmark index .TASI rose 0.2%, with ACWA Power 2082.SE rising 6.5%, while Elm Co 7203.SE jumped 10% following a steep rise in first-quarter profit.

Dubai's main share index .DFMGI gained 0.8%, led by a 7.8% surge in Emirates Central Cooling Systems EMPOWER.DU after an upbeat quarterly earnings.

Meanwhile, the United Arab Emirates said on Wednesday that its ties and its international and defense partnerships were a "purely sovereign matter," rejecting an earlier statement by Iran saying that Abu Dhabi's cooperation with the U.S. threatened Iran's security and national interests.

In Abu Dhabi, the index .FTFADGI was up 0.3%, with Abu Dhabi Islamic Bank ADIB.AD rising 1.4%.

The Qatari index .QSI added 0.2%.