ROME—A meeting on Tuesday between Pope Francis and Iranian President Hassan Rouhani will showcase a long-standing relationship between the Vatican and Iran that has grown closer under the current pontificate and could help support efforts for peace in Syria and Iraq.

Pope Francis and Mr. Rouhani will meet during the second day of the Iranian president’s four-day visit to Italy and France, his first overseas trip since the loosening of sanctions earlier this month, following last year’s Iranian nuclear deal with six world powers. The two men are likely to discuss efforts for peace in Syria and Iraq.

Having extolled the role of Iran in finding a solution to the conflict in Middle East, the Vatican is apt to soft-pedal criticism of human rights issues in Iran during Tuesday’s meeting.

Pope Francis can help promote the “thaw in diplomatic relations between Iran and other countries” in a way similar to his support for a rapprochement between Cuba and the U.S., Father Bernardo Cervellera, editor of the Rome-based Asia News, said. “If we want peace in the Middle East, Iran and Iranian Islam have a vital role to play.”

The meeting will be the first between a pope and an Iranian head of state since 1999, when President Mohammad Khatami visited St. John Paul II. Yet diplomatic relations between the two states, which predate the 1979 Islamic revolution in Iran, have been consistently cordial and have grown more so in the current pontificate.