Abbas said he was delighted to visit the Vatican and meet with the Catholic leader for the first time, the Palestinian news agency WAFA reported.
"I am so honored to meet with you here and hope that you feel at home," Pope Frances said.
Among other things, the pope and Abbas discuss the situation in the Middle East, particularly Israeli-Palestinian negotiations, Vatican Radio reported. The two expressed hope that this process would be successful in reaching a lasting, peaceful solution to the conflict.
Other Palestinian officials and dignitaries also attended the meeting, WAFA said.