June 2 (Reuters) - Major Gulf stock markets were mixed in early Tuesday trading, as investor sentiment remained cautious amid uncertainty over the progress of U.S.-Iran peace talks.

On Monday, U.S. President Donald Trump said negotiations with Iran were still underway, despite an earlier report by Iran's Tasnim news agency claiming Tehran had suspended the indirect talks with Washington.

Trump also said on Monday that, through intermediaries, he had communicated with the Iran-backed Lebanese militia Hezbollah and had obtained assurances the group would not launch an attack on Israel.

Saudi Arabia's benchmark index .TASI eased 0.1%, hit by a 0.9% fall in oil behemoth Saudi Aramco 2222.SE.

Brent crude futures LCOc1 lost 53 cents, or 0.56%, to $94.45 a barrel at 0649 GMT. O/R

Dubai's main share index .DFMGI dropped 0.4%, with top lender Emirates NBD ENBD.DU retreated 1.3%.

In an interview with CNBC, Trump said he would not be concerned if the talks ended. However, he later said in a social media post that discussions were continuing. He also told ABC News that he expected an agreement to be reached within the next week.

In Abu Dhabi, the index .FTFADGI was flat in choppy trading.

The Qatari index .QSI added 0.3%, with the Gulf's biggest lender Qatar National Bank QNBK.QA gaining 0.5%.