* Kuwait seen as potential bridge between Iran, S.Arabia
* Tehran's nuclear engagement welcomed by neighbours
* But rivalry with Sunni power Riyadh still strong
DUBAI, June 1 Kuwait's emir began a visit to Iran on Sunday, the first by a ruler of the U.S.-allied Gulf Arab state since the 1979 Islamic revolution, underscoring improving ties between Tehran and its Arab neighbours.
Regional television stations showed Iranian President Hassan Rouhani escorting Sheikh Sabah al-Ahmed al-Sabah to review an Iranian honour guard upon the emir's arrival in Tehran.
Rouhani, elected last year, has been trying to lead Shi'ite Muslim Iran out of years of isolation and his decision to engage with world powers in talks about Tehran's nuclear programme has been welcomed by some in the Sunni Muslim states on the other side of the Gulf.
Kuwait, home to a sizeable Shi'ite Muslim minority, is seen by some as a potential bridge between Iran and the Gulf Arab states, including the main power Saudi Arabia, with which relations remain strained, not least because of opposing stances over Syria's civil war.
Iranian Foreign Minister Javad Zarif said on Sunday he could not take up an invitation to visit Saudi Arabia to attend a conference to attend a meeting of the Organisation of Islamic Cooperation later this month because the proposed dates clashed with planned nuclear negotiations with world powers.
Sheikh Sabah, a former Kuwaiti foreign minister, is described by analysts as one of the region's most active diplomats, often acting as a mediator.
The emir's visit comes at "a critical time and amid complicated changes in the region," said Ali Anayati, Iran's ambassador to Kuwait, Kuwaiti news agency KUNA reported. He said the visit would start a "new chapter of bilateral cooperation".
Both leaders want to "create a safe and stable regional system based on non-interference in other countries' internal affairs," he said.
The emir heads a delegation which includes the foreign minister and oil minister, Iranian news agency IRNA said.
The visit follows Foreign Minister Zarif's tour of the Middle East in December after Tehran signed an interim nuclear deal with world powers. Kuwait said it hoped the deal would help regional stability and security.
Saudi Arabia, which backs rebels fighting Syrian President Bashar al-Assad, a close ally of Iran, sees the Shi'ite power as one of its biggest threats.
Gulf Arab states, like Western powers, suspect Iran has been using its nuclear power programme as a front to develop weapons capability.
Bahrain and Saudi Arabia have also accused Iran of stirring up their Shi'ite communities to revolt. Iran says its nuclear programme is peaceful and denies interference in those countries' affairs. (Reporting by Sylvia Westall and Sami Aboudi; Editing by Robin Pomeroy)