Francis told the imam: 'The meeting is the message.'
It comes five years after the Cairo-based Al-Azhar froze talks with the Vatican to protest comments by then-Pope Benedict XVI.
Benedict had demanded greater protection for Christians in Egypt after a New Year's bombing on a Coptic Christian church in Alexandria killed 21 people.
Since then, Islamic attacks on Christians in the region have only increased, but the Vatican and Al-Azhar nevertheless sought to rekindle ties, with a Vatican delegation visiting Cairo in February and extending the invitation for el-Tayyib to visit.
Francis and el-Tayyib spoke privately for 25 minutes in the pope's private library, bidding each other farewell with an embrace.
El-Tayyib and his delegation then had talks with the Vatican cardinal in charge of inter-religious dialogue.
The Vatican said the meeting held a 'great significance' for Catholic-Muslim dialogue.
In a statement, spokesman the Reverend Federico Lombardi said Francis and el-Tayyib discussed the need for 'authorities and the faithful of the world's great religions to show a common commitment to peace in the world'.
They also discussed the rejection of violence and extremism, and the plight of Christians 'in the context of conflicts and tensions in the Mideast and their protection,' the statement said.
After the audience, el-Tayyib travels to Paris to open a Muslim-Catholic conference on East-West relations.
The Vatican's relations with Islam hit several bumps during Benedict's papacy. He outraged Muslims with a 2006 speech quoting a Byzantine emperor as saying some of the Prophet Muhammad's teachings were 'evil and inhuman'.
The subsequent suspension of talks with Al-Azhar institutionalized the bad blood.
El-Tayyib, however, sent a message of congratulations to Francis upon his 2013 election and said he hoped for renewed cooperation.
Francis responded, and has made clear over the course of his three-year pontificate that relations with Islam are a top priority.
In a recent interview with the French Catholic newspaper La Croix, Francis took a conciliatory line toward Islam, saying 'I sometimes dread the tone' when people refer to Europe's 'Christian' roots.
'It is true that the idea of conquest is inherent in the soul of Islam,' he said.
But he added that Christianity, too, had its 'triumphalist' undertones. 'It is also possible to interpret the objective in Matthew's Gospel, where Jesus sends his disciples to all nations, in terms of the same idea of conquest.'
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Pope for president

End time Pope

Before the end of 4years we will know why pope francis was elected as pope in place of bennedict.

I hope it is not what i am thinking