He noted that many Catholic Islam experts had already hailed the initiative and that a positive response by Yale University Divinity School had been endorsed by about 300 Christian leaders of various churches in the United States.
The Pontiff agreed to receive Jordanian Prince Ghazi bin Mohammad bin Talal, head of the Royal Aal al-Bayt Institute for Islamic Thought that is coordinating the initiative, and a small group of signatories to discuss the issue.
"At the same time, a working meeting could be organised between your delegation and the Pontifical Council for Interreligious Dialogue" and other Catholic Islam experts, Bertone wrote.
The meeting will be a milestone for Pope Benedict, who sparked Muslim protests last year with a speech hinting Islam was violent and irrational.
He repeatedly expressed regret for the reaction to the speech, but stopped short of a clear apology sought by Muslims.
The Pontiff noted the "positive spirit" of the Muslim scholars' letter, which quoted from the Koran and the Bible to show both Christianity and Islam considered love of God as their greatest commandment and love of neighbour as the second.
"Such common ground allows us to base dialogue on effective respect for the dignity of every human person, on objective knowledge of the religion to the other," the Vatican wrote.
Catholic experts on Islam say there is still so much misunderstanding between Christians and the world's 1.3 billion Muslims about what each other believed that a serious dialogue about them would help improve relations.
If it comes about, the Christian-Muslim dialogue could also pose challenges to Christians, who have a wide variety of views about Islam and the Muslim world would have to work together in responding to the Muslim scholars' initiative.
London Cardinal Cormac Murphy-O'Connor called last week for a meeting of all Christian leaders to discuss issues facing them, but the Vatican was not enthusiastic, Church officials said.
