Pope Francis on Monday described his meeting with top cleric Grand Ayatollah Ali Sistani as "good for my soul", as he returned to Rome following his historic trip to Iraq.

Speaking to journalists on board his plane, the 84-year-old pontiff described Sistani -- one of Shiite Islam's top clerics -- as "a wise man".

"That meeting was good for my soul," he said after the first-ever papal visit to Iraq.

"I felt the need to make this pilgrimage of faith and penitence and to go and find a great, wise man, a man of God -- you could tell that just by listening to him," Francis added.

"He is a person with this wisdom but also prudence. He told me that for the last 10 years, he has not received any visitors with political or cultural objectives, only those with religious motives.

"He was very respectful during our meeting and I felt honoured. He never gets up to greet visitors, but he got up to greet me twice."

Two years ago, the pope signed a document on "human fraternity for world peace and living together", with leading Sunni cleric Sheikh Ahmed al-Tayeb, the grand imam of Al-Azhar.

No such text was agreed with Sistani, who represents the other main branch of Islam, but the pope said there would be "other steps" in his continued dialogue with Islam.

"We must move forward with other religions," said the pope.

He referenced criticism of his approach by some Catholic traditionalists, who worry about seeing all religions on the same level.

"There are some critics who say that the pope is not courageous, that he is unconscious, that he takes steps outside Catholic doctrine, that he is one step away from heresy," the pope said.