* Iran FM on charm offensive in Egypt, meets top cleric
* Cairo sees Syria as the key to better ties with Iran
By Maria Golovnina and Tom Perry
CAIRO, Jan 10 (Reuters) - Shi'ite Iran, increasingly isolated over its nuclear programme, tried to improve ties with Egypt on Thursday, playing down differences over Syria and seeking to reduce sectarian tensions by courting the country's top Sunni scholar.
Iran has been at odds with the Arab world's most populous nation since Tehran's Islamic revolution in 1979. But a new era of Egyptian politics that followed the 2011 overthrow of Hosni Mubarak has led to more contacts.
In Cairo for talks with President Mohamed Mursi and others, Iranian Foreign Minister Ali Akbar Salehi praised Egypt's revolution and its new, Islamist-led government.
He also met Sheikh Ahmed Al-Tayeb, the Grand Sheikh of Al-Azhar - one of the most prestigious seats of learning in the Sunni world.
The two men stressed the importance of Muslim unity and Salehi said there were no differences between Muslims, whether they were Sunnis or Shi'ites.
"Egypt and Iran are among the most important states in the Middle East, with influence in the region, and they can complete each other in the fields of economy and trade," Salehi told Egyptian state television in an interview.
During his 30 years in power Mubarak was deeply suspicious of Islamist-led Iran and never visited Tehran.
The countries took opposite paths: Egypt concluded a peace treaty with Israel while becoming a close ally of the United States and Europe, while Iran positioned itself as the centre of opposition to Western influence in the region.
In a break from the Mubarak era, Mursi went to Tehran last year in one of his first official trips as leader.
But Syria remains the main stumbling block. Tehran is one of the last and staunchest allies of Syrian President Bashar al-Assad, whereas Egypt wants Assad to relinquish power to stop the protracted civil war. Analysts said Mursi believes Iran's ties with the Arab world hinge on a review of its support for Assad.
Addressing reporters after talks, Salehi and his Egyptian counterpart Mohamed Kamel Amr sought to sidestep thorny issues and instead emphasised their common goals.
Salehi dismissed the notion of Sunni-Shi'ite tensions in regional affairs, describing it as an invention of Western media. He conveyed President Mahmoud Ahmadinejad's greetings to Mursi, and said the Egyptian leader had been invited to Iran again.
" The neighbouring states and the states of the region must seek a way to solve to the Syrian issue in a Syrian-Syrian way," Salehi said.
Yet, with their positions on Syria diametrically different, it is unclear how much real progress Iran's new charm offensive could achieve. No trade or cooperation agreements were signed as part of Salehi's visit.
Suspected by the West to be developing a nuclear bomb - which it denies - Iran has found itself increasingly isolated due to economic sanctions and a diplomatic push against it.
It desperately needs new friends in the region, particularly since Israel and the United States have not ruled out military action against Tehran.
The Mursi administration has included Iran in a regional initiative on Syria, though so far efforts to bring together Iran, Saudi Arabia and Turkey have made no obvious progress.
"Some might see that this initiative is not moving, but in truth the contacts are continuing at different levels and it is still, in truth, the initiative that can bring fruit and halt the bloodshed," said Amr.
"We still see that Iran is a party in the quartet initiative and has a role that it can play."