July 5 (Reuters) - Most Gulf stock markets closed lower on Sunday as investors grew more cautious following a lack of progress in indirect talks between Iran and the United States.

There were no signs that the two sides had made progress toward a lasting peace in the talks that concluded on Wednesday, which instead focused on issues they said had been resolved when they announced an interim agreement two weeks earlier.

The Qatari Foreign Ministry said the next meeting will be held after the funeral of Iran’s late Supreme Leader Ayatollah Ali Khamenei, who is scheduled to be buried on July 9.

The Saudi market's benchmark index fell 0.3 percent, impacted by a 0.5 percent drop in Al Rajhi Bank's shares.

Meanwhile, Saudi Arabia’s non-oil private sector recorded stronger growth in June, driven by the fastest increase in new business in four months.

However, a survey conducted today showed that companies are still facing rising costs and declining demand for exports.

In Qatar, the index rose 0.3 percent, with Qatar National Bank shares climbing 0.2 percent.

The Iranian commercial attaché in Doha told state media today that maritime trade between Iran and Qatar has resumed after a hiatus of about five months.

The Kuwaiti index fell 0.3 percent, the Omani index dropped 0.2 percent, and the Bahraini index lost 0.6 percent.

Outside the Gulf region, Egypt's blue-chip index rose 1.2 percent, driven by a 1.9 percent gain in Commercial International Bank shares.

Data from the Central Bank of Egypt indicated that the money supply (M2) grew by 19.6 percent year-on-year in May, to 15.33 trillion Egyptian pounds ($312.35 billion).