By Ateeq Shariff

July 2 (Reuters) - Most major Gulf stock markets were nearly flat in early trading on Thursday after Iran and the United States wrapped up a round of indirect talks with no sign of progress toward a lasting peace agreement.

Iranian and U.S. negotiators spent two days in Doha addressing maritime traffic in the Strait of Hormuz and the unfreezing of Iranian assets, two central elements of the initial accord, according to sources familiar with the talks.

The next round of negotiations will take place after funeral rites for Iran's late Supreme Leader Ayatollah Ali Khamenei, who is set to be laid to rest on July 9, Qatar's Foreign Ministry said.

Saudi Arabia's benchmark index .TASI eased 0.1%, with petrochemical maker Industries Qatar IQCD.QA losing 1.1%.

Meanwhile, speaking in Washington, President Donald Trump said negotiations were advancing on possible restrictions to Iran's nuclear program, the main issue underpinning the war launched by the United States and Israel in February.

"The denuclearization of Iran is moving along well," he said. "They've had very good meetings, and we'll see."

Dubai's main share index .DFMGI was flat in choppy trade.

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

The Qatari index .QSI lost 0.3%, weighed down by a 0.9% fall in the Gulf's biggest lender Qatar National Bank QNBK.QA.