June 4 (Reuters) - Major Gulf stock markets rose slightly in early trading on Thursday after Israel and Lebanon agreed to implement a ceasefire, boosting optimism for a wider deal to end the U.S. war with Iran even as tensions simmered.

The Israel-Lebanon ceasefire is contingent on a complete cessation of fire from the Iran-aligned Hezbollah militia and the evacuation of all its operatives from the South Litani Sector, a joint statement released by the U.S. State Department said following negotiations in Washington.

U.S. President Donald Trump suggested on Wednesday that there could be progress in negotiations with Iran as soon as this weekend.

Earlier, Iran struck Kuwait, damaging its airport and injuring dozens while the U.S. military carried out strikes near the Strait of Hormuz.

Markets stayed cautious as attention returned to developments involving Iran and the Strait of Hormuz after a period of easing tensions and perceived progress in negotiations, said Ahmad Assiri, research strategist at Pepperstone.

Saudi Arabia's benchmark index .TASI added 0.1% in choppy trade.

Dubai's main share index .DFMGI gained 0.3%, with sharia-compliant lender Dubai Islamic Bank DISB.DU rising 1.3% and toll operator Salik SALIK.DU adding 1.3%.

In Abu Dhabi, the index .FTFADGI was up 0.2%.

The Qatari index .QSI added 0.3%, with petrochemical maker Industries Qatar IQCD.QA putting on 0.3%.

Meanwhile, Brent futures LCOc1 were down 87 cents, or 0.89%, at $96.92 a barrel by 0458 GMT.