Vatican City (AFP) - Pope Francis embraced the grand imam of Cairo's Al-Azhar Mosque at the Vatican on Monday in a historic encounter both sides hope will lead to greater understanding and dialogue between the two faiths.

The first Vatican meeting between the leader of the world's Catholics and the highest authority in Sunni Islam marks the culmination of a significant improvement in relations between the two faiths since Francis took office in 2013.

"Our meeting is the message," Francis said in a brief comment at the start of his meeting with Sheikh Ahmed al-Tayeb, shortly after he had hugged and kissed his guest, Vatican officials told a small pool of reporters covering the event.

In a statement on the trip, Al-Azhar, an institution that also comprises a prestigious seat of learning, said the two sides had agreed to convene a "peace conference".

A statement quoted Tayeb as telling Francis: "We need to take a joint stance, hand in hand, to bring happiness to humanity. Divine religions were revealed to make people happy, not to cause them hardship."

The imam's deputy, Abbas Shuman, told Egyptian TV channel CBC that the two leaders had agreed to resume dialogue and that the proposed conference would cover the issues of poverty, extremism and terrorism.

The Vatican did not immediately confirm the conference plans. A spokesman said the talks had been "very cordial" with the imam spending 30 minutes with the pope and just over an hour in total at St Peter's.

Tayeb's decision to fly to Rome, unexpectedly announced last week, followed the easing of serious tensions that marked the reign of Francis's predecessor, Benedict XVI.

Ties were badly soured when the now-retired Benedict made a September 2006 speech in which he was perceived to have linked Islam to violence, sparking deadly protests in several countries and reprisal attacks on Christians.

Pope John-Paul II met the then-grand imam of Al-Azhar in Cairo in 2000, a year before the September 11 attacks on New York transformed relations between the West and the Islamic world.

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Monday's visit was effectively the long-delayed reciprocal meeting and the Vatican said that both clerics had "underlined the great significance of this new meeting".

Vatican spokesman Federico Lombardi said in a statement that the pope and the imam had "mainly addressed the common challenges faced by the authorities and faithful of the major religions of the world."

These included working together for world peace, rejecting violence and terrorism, and the situation and protection of Christians against a backdrop of conflict and terrorism in the Middle East."

- Promoting 'true Islam' -

The pope presented the imam with a copy of his recent encyclical, Laudato Si', a letter to the faithful in which he urges the world to wake up to the threat posed by climate change and economic inequality.

Tayeb decided to accept the invitation to Rome as a result of the numerous conciliatory gestures Francis has made to the Muslim world since being elected in early 2013.

"If it were not for these good positions the meeting would not be happening," Shuman told AFP on Sunday, adding that the imam wanted to promote "true Islam and to correct misunderstandings created by extremist terrorist groups."

"He encourages countries not to deal with their Muslim citizens as groups that present a threat," Shuman said.

"And he encourages Muslims in Western society to meld with their societies... it is a message for both sides."

After the tensions of the Benedict years, Francis moved quickly to set a new tone, sending a personal message to the Muslim world to mark the end of the first month of Ramadan of his pontificate.

The Argentinian pontiff followed up by pushing various inter-faith initiatives and he was accompanied by both Rabbi Abraham Skorka and Islamic studies professor Omar Abboud when he visited Jordan and Israel in 2014.

But perhaps the gesture that clinched the deal was the most dramatic piece of political theatre of his papacy: his April visit to the migrant crisis island of Lesbos which concluded with him bringing three Syrian Muslim families back to the Vatican.