Saleh met with Pope Francis, the Vatican secretary of state and foreign minister during back-to-back audiences Saturday, his second visit to the Vatican.
The Holy See says the meetings focused on promoting peace and security in Iraq, especially for Christian minorities, many of whom have fled communities that date from the time of Christ to escape persecution by Islamic State militants.
In a statement, the Vatican said the meetings covered the "importance of preserving the historical presence of Christians in the country, of which they are an integral part, and the significant contribution they bring to the reconstruction of the social fabric, highlighting the need to guarantee their security and a place in the future of Iraq."
Francis had expressed hope of visiting Iraq this year, but no trip has been confirmed and it's unclear if it will be given the turmoil unleashed by the U.S. drone strike on Iraqi soil that killed a top Iranian general.
The attack provoked the ire of Iraqi officials and led to the passing of a non-binding resolution by Iraqi lawmakers to oust U.S. troops.
The Vatican hinted at the rising tensions, saying the discussions underlined the need for the international community to "re-establish trust and peaceful co-existence."
During the meeting, Saleh gave Francis a replica of the Code of Hammurabi, the ancient set of Babylonian laws, calling it a "symbol of peace."
Francis, for his part, gave Saleh a medallion and a set of his major teaching documents, including one on Christian-Muslim fraternity. He told Saleh he wanted an Iraqi identity card identifying him as a descendant of Abraham, a figure common to Christianity, Islam and Judaism.