The refugees picked by Pope Francis to be taken in by the Vatican have praised him as their "saviour" after being offered the chance of a new life in Italy.

"We saw friends and relatives die in the rubble, we fled Syria because we no longer had any hope," said Hasan, from Damascus.

Speaking to Italian daily La Stampa, he shared how he, his wife and two-year-old son crossed the sea from Turkey to Greece on an overloaded rubber dinghy.

They were among 12 refugees, all of them Muslims, to be taken to the Vatican following the Pope's trip to Lesbos over the weekend.

It was meant as a symbolic gesture to indicate Francis' solidarity with those suffering as a result of fleeing war and persecution in countries like Syria, Iraq and Eritrea. "All refugees are children of God," he said on the flight back to Rome, adding that the decision to bring the refugees with him was "an inspiration of the Holy Spirit".

A statement from the Holy See press office confirmed the Vatican will take responsibility for all three families, who are expected to seek asylum in Italy.

"What's happening with us, it's like a dream," Hasan's wife, Nour, told NBC News on Sunday. "It's like a beautiful dream."

Another couple, Osama and Zamalka, also from Damascus and chosen by Francis with their eight- and six-year-old children, said: "Francis gave us new life".

"I still don't believe we are here now," Osama told reporters. "He [the Pope] is the father of peace in the world, and peace has no religion."

A third family fled Deir Ezzor in Syria, which is now occupied by ISIS. "We discuss a lot and find it hard to imagine what life will be like in the future: we don't know whether we will start over in Europe or whether, one day, we will be able to return to a Syria free of war and violence," said Ramy, a 51-year-old teacher.

He, his wife Suhlia and their three children, aged between seven and 18, are indebted to the Pope, he added.

"We are grateful to the Pope, we will prove ourselves worthy of this opportunity and the gift he gave us."

Suhlia told NBC: "He saved our lives. To me, he is now like an angel, a new father who saves the lives of his children."

"I spoke to him, but I don't even remember what I told him," she added. "I was overwhelmed with emotions. No Muslim leader has done what he has done."

Pope Francis' trip to Lesbos was organised after the Pontiff said he wanted "to shed light on the major humanitarian problem" presented by the refugee crisis.

Speaking to reporters afterwards, he said the three families were selected because they had their papers ready.

Two Christian families were also originally meant to be taken in by the Vatican, but their documents had not been prepared in time.

"I have always said that building walls is not a solution," the Pope added. "We saw walls during the last century and they did not resolve anything. We must build bridges. Bridges are built with intelligence, with dialogue, with integration."

In Lesbos, he greeted hundreds of refugees. "I want to tell you that you are not alone," he told them.

"In these weeks and months, you have endured much suffering in your search for a better life. Many of you felt forced to flee situations of conflict and persecution for the sake, above all, of your children, your little ones."