Pope Francis held talks with Mr Abbas in the Vatican on Saturday, where he expressed their hopes for a resumption of peace negotiations between Palestine and Israel and for "courageous decisions" for peace, with international support.
Francis also presented Mr Abbas with a medallion representing an angel of peace, telling the Palestinian leader he thought of him "as an angel of peace".
A Vatican statement described the talks as "cordial," and said the two sides "expressed great satisfaction with the agreement reached on the text of a comprehensive agreement between the Parties concerning essential aspects of the life and activity of the Catholic Church in Palestine, which will be signed in the near future."
Mahmoud Abbas will attend Sunday's canonization Mass for two Palestinian Blessed, for which he also thanked Pope Francis.
A Vatican statement said: "On Sunday President Abbas will attend the canonisation of the two Palestinian nuns, for which he thanked the Holy Father.
"During the cordial discussions, great satisfaction was expressed for the accord reached on the text of a comprehensive Agreement between the Parties on various essential aspects of the life and the activity of the Catholic Church in Palestine, to be signed in the near future.
"Attention then turned to the peace process with Israel, and the hope was expressed that direct negotiations between the Parties be resumed in order to find a just and lasting solution to the conflict.
"To this end the wish was reiterated that, with the support of the international Community, Israelis and Palestinians may take with determination courageous decisions to promote peace. Finally, with reference to the conflicts that afflict the Middle East, and in reaffirming the importance of combating terrorism, the need for interreligious dialogue was underlined."
