Story highlights Mariam Yehya Ibrahim and her family meet Pope Francis, thank him for his prayers

Francis thanks Ibrahim and her family for their "courageous constant witness to faith"

Ibrahim and her family will be in Italy for a short time before traveling on to the United States

"Today is a day for celebration," says Italian Prime Minister Matteo Renzi

Mariam Yehya Ibrahim, the Sudanese Christian woman sentenced to death in Sudan because of her faith, arrived in Rome on Thursday, the Italian Foreign Ministry said.

Ibrahim "will remain in Italy for a short time and then will travel on to the United States," the ministry said.

Sudanese authorities had said Ibrahim was guilty of rejecting Islam in favor of Christianity, but her conviction for "apostasy" and adultery was overturned last month on appeal, following weeks of international controversy.

After her release, she and her husband, American Daniel Wani, were detained for two days, accused of falsifying travel documents after going to the airport in Sudan's capital, Khartoum. They were trying to fly to the United States with their baby daughter, who was born while Ibrahim was in prison, and toddler son.

Now their dream of starting a new life in the United States appears to be on the verge of becoming reality.

Not only that, but Ibrahim and her family met with Pope Francis at his private residence in Domus Santa Marta in Vatican City.

During the meeting Thursday, which lasted about half an hour, Ibrahim thanked the Pope for his and the Roman Catholic Church's support and prayers, the Vatican said.

He, in turn, thanked Ibrahim and her family for their "courageous witness and constancy of faith."

Francis also played with the children, 18-month-old Martin and 2-month-old Maya, and greeted the Italian diplomats involved in her journey to Italy.

With this gesture, the Vatican said, the Pope "desired to show his closeness, attention and prayer also to all those who suffer for their faith, in particular to Christians who are enduring persecution or limitations imposed upon their religious freedom."

Ibrahim has said that her mother, an Ethiopian Orthodox Christian, raised her as a Christian.

She remained steadfast in her faith despite the threat of a death sentence, saying at her sentencing hearing in May: "I am a Christian, and I will remain a Christian."

'Day for celebration'

Ibrahim and her family were earlier greeted at the airport in Rome by Italian Prime Minister Matteo Renzi.

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In a brief statement to reporters at the airport, Renzi said, "Today we are very happy. ... Today is a day for celebration."

Speaking alongside him, Deputy Minister of Foreign Affairs Lapo Pistelli said Ibrahim and her children were well and in "excellent condition."

He said Pope Francis had been informed Wednesday by the Prime Minister that the family was coming to Italy, and that the government had worked to bring about a meeting between them.

"Mariam and her two children will have important meetings in the following days and then they will travel to the United States."

How Italy helped

Pistelli said Italy had become involved in the case because, as a Catholic country, it was very moved by Ibrahim's story and wanted to help.

Italy has good relations with Khartoum and offered to help the U.S. Embassy there to speed up the process of getting U.S. passports for Ibrahim and her family to leave the country, the minister said.

Pistelli said he had traveled to Sudan two weeks ago to start the process but it was not finalized until Wednesday night.

He posted an image to his Facebook page of himself with Ibrahim and the two children, apparently taken on board the plane shortly before their arrival in Rome. "Mission accomplished," he wrote.

Ibrahim, her husband and their two children are now in a protected government house, he said. It is unclear how long Ibrahim will stay in Rome before flying on to the United States, he said, adding that it had to do with passport procedures.

CNN has not yet been able to reach the U.S. Embassy or the Sudanese Foreign Ministry for comment.

Persecution claim

Ibrahim's ordeal began when one of her relatives, a Muslim, filed a criminal complaint saying her family was shocked to find out she had married Wani, a Christian, after she was missing for several years.

A Sudanese court considered Ibrahim a Muslim because her father was Muslim. She was charged with adultery, because a Muslim woman's marriage to a Christian man is illegal in Sudan. She was also charged with apostasy, accused of illegally renouncing what was alleged to be her original faith.

She insists she has never been a Muslim -- and says she was persecuted as a Christian while in prison.

Convicted when she was about eight months pregnant, she gave birth two weeks later while shackled.

On Monday, a Sudanese Islamic jihadi group which has previously claimed an attack on a Sudanese journalist released a statement threatening Ibrahim.

The group vowed to carry out what it said was the justified death sentence against Ibrahim that was repealed by a higher court.

Amid this threatening environment, Daniel Wani told CNN that his family had reported seeing unknown people outside their old residence in Khartoum. Their numbers had been increasing over the past few days, he said.