CAIRO, April 28 (Reuters) - Senior aides to Egyptian President Mohamed Mursi made a rare visit to Tehran for talks with Iran on an Islamic initiative to seek a peaceful solution to Syria's civil war, the two sides said on Sunday.

Tehran is Syria's closest ally and has provided money, weapons, intelligence and training for President Bashar al-Assad's forces, while Egypt has given political support to the opposition Syrian National Coalition fighting to oust him.

Mursi's foreign affairs adviser Essam Haddad and his chief-of-staff Rifaa El-Tahtawy met Iranian officials in a follow-up to Iranian President Mahmoud Ahmadinejad's groundbreaking visit to Cairo in February for an Islamic summit.

An Iranian Foreign Ministry statement said they agreed on "the necessity of an action plan...to act on the Egyptian president's plan on the Syria crisis through an acceptable political solution which can help end the violence and help national reconciliation with the participation of the people of Syria".

Mursi included Iran, alongside Egypt, Saudi Arabia and Turkey, in a diplomatic "Islamic Quartet" of countries established last year to try to broker a solution in Syria.

The Egyptian leader proposed negotiations between Syrian government representatives not directly involved in repression and opposition leaders under regional or U.N. auspices on a transition of power.

However, the Saudis stayed away from the group in February in apparent irritation at the inclusion of the Iranians, and Syria has rejected foreign involvement in the national dialogue proposed by Assad.

The visiting Egyptian officials met Ahmadinejad and senior figures in Iran's foreign policy establishment - national security adviser Saeed Jalili, Foreign Minister Ali Akbar Salehi and Ali Akbar Velayati, foreign policy adviser to Supreme Leader Ayatollah Ali Khamenei.

"The relationship between Cairo and Tehran is extremely sensitive, and should be managed wisely. And this is what Egypt is doing," Haddad said on a television talk show broadcast on Saturday.

The two countries do not have full diplomatic relations, which were broken off after Egypt gave sanctuary to the deposed shah following Iran's 1979 Islamic revolution and signed a peace treaty with Israel in the same year.

Ties have thawed gradually since the 2011 uprising that toppled Egyptian President Hosni Mubarak, but ultraconservative Sunni Salafists in Egypt protested against the launch of tourist flights with Iran, prompting the government to suspend the plan.

The Salafis contend that Iran is trying to spread Shi'ite Islam in Sunni Muslim countries such as Egypt, a charge that Tehran denies. (Additional reporting by Yeganeh Torbati in Dubai and Alexander Dziadosz in Cairo; Writing by Paul Taylor: Editing by Angus MacSwan)