Pope Francis has met with Iran's President Hassan Rouhani in a private audience at the Vatican.

Rouhani is on a four-day visit to Italy and France aimed at building diplomatic and commercial relationships.

The visit follows the enactment of a historic nuclear deal which saw Iran demolishing much of its capacity to produce weapons-grade nuclear material in return for a lifting of the sanctions that have crippled its growth.

The meeting at the Vatican was the first between a Pontiff and an Iranian leader since 1999. It lasted for around 40 minutes.

According to the Catholic News Service it concluded with the Pope saying: "I thank you very much for this visit. I have high hopes in peace."

In response, President Rouhani asked Francis to pray for him and wished him well.

A statement by the Vatican said the two discussed Iran's role in finding political solutions to the strife in the Middle East and stopping the spread of terrorism.

Pope Francis also raised the question of the "promotion of human dignity and freedom of religion".

In an earlier speech, Rouhani quoted the Qur'an, saying that "the church, the synagogue and the mosque must live side by side". He added: "It lists them in that order – with the church first and the mosque last. This is no coincidence."

Rouhani gave the Pope a book of reproductions by painter Mahmoud Farshchian and a rug made in the Shi'ite holy city of Qom.

In return, the Pope gave him a copy of his encyclical on the environment and a medal showing St Martin using his cape to cover a poor man. Francis described this as a "sign of brotherhood".