Talks between the Vatican and Al-Azhar were suspended by the Muslim university in 2011 following a series of remarks made by now-retired Pope Benedict XVI.
Greiche spoke to Catholic News Service in Cairo Dec. 4, a day after Comboni Father Miguel Ayuso Guixot, secretary of the Pontifical Council for Interreligious Dialogue, met at the prominent Muslim university with Abbas Shouman, deputy to Al-Azhar's grand imam, Sheik Ahmad el-Tayeb.
"There was a meeting in a positive atmosphere, and both (sides) agreed to continue," Greiche said.
A decades-old dialogue between Al-Azhar and the Vatican started to fray in 2006, after Pope Benedict gave a speech in Regensburg, Germany, which Al-Azhar officials and millions of Muslims said linked Islam to violence.
Al-Azhar halted the talks altogether in 2011 after the former pope said Christians in the Middle East were facing persecution.
Greiche told Catholic News Service that no dates or details for any future talks were set in the Dec. 3 meeting, which included the Vatican's Ambassador to Egypt, Archbishop Jean-Paul Gobel, and Al-Azhar's advisor on dialogue, Mahmoud Azab.
In statements sent to CNS a day after the meeting, Azab said that "the coming period will witness amendments to the agreements" governing the dialogue between Al-Azhar and the Vatican, aimed at enabling "a unified stance and vision on ways of dealing with issues." Azab said this would involve "the removing of obstacles within those agreements," but he did not elaborate.
However, in a November interview with CNS last month, Azab reiterated Al-Azhar claims that Pope Benedict had offended Islam and Muslims with the 2006 speech, and later again in 2011 when the former pontiff focused only on the suffering of Christians due to violence in the Middle East region, which Azab said many Muslims were suffering from as well.
In his Dec. 4 statements, Azab said, "The grand imam has a lot of optimism that, with Pope Francis, there is wide terrain for equal dialogue and mutual respect."