"Sheikh Sabah al-Ahmed al-Sabah... Arrived in Riyadh this evening," the official Saudi Press Agency said, adding that Qatar's Sheikh Tamim bin Hamad al-Thani had also reached the Saudi capital.
Kuwait's official news agency KUNA had earlier reported that country's emir had left for Saudi Arabia to meet fellow "leaders of the Gulf Cooperation Council (GCC) states".
The United Arab Emirates vice president, Sheikh Mohammed bin Rashid al-Maktoum, also arrived in Riyadh, according to SPA, while the Bahrain News Agency said King Hamad was due to leave for Riyadh today to attend a meeting of GCC leaders.
Sheikh Sabah has been leading a mediation effort to bridge the gap between GCC members Qatar and Saudi Arabia, the United Arab Emirates and Bahrain.
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Qatar is accused by other GCC members of supporting the Muslim Brotherhood and offering a safe haven to other banned Islamist groups.
Saudi Arabia, the UAE and Bahrain all withdrew their ambassadors to Doha in March, sparking one of the GCC's worst diplomatic rows since its creation in 1981.
"We hope the Riyadh meeting today (Sunday) comes to a happy ending that strengthens the GCC," he said.
The dispute has led to reports of the venue for the annual GCC summit being moved from Doha, although Kuwait last week denied any change.
A GCC foreign ministers' meeting which was scheduled on November 10 to prepare for the summit was postponed.
Saudi Arabia, Bahrain and the UAE have accused Qatar of meddling in their internal affairs by supporting the Brotherhood.
Doha earlier this year asked Brotherhood leaders to leave Qatar following diplomatic pressure from Saudi Arabia.