The question has been swirling around ever since Francis laid his hands on the head of a young man after celebrating Mass in St Peter's Square on Sunday.
The young man heaved deeply a half-dozen times, shook, and then slumped in his wheelchair as Francis prayed over him.
The television station of the Italian bishops' conference said it had surveyed exorcists, who agreed there was "no doubt" that Francis either performed an exorcism or a prayer to free the man from the devil.
The Vatican was more cautious on Tuesday, saying Francis "didn't intend to perform any exorcism. But as he often does for the sick or suffering, he simply intended to pray for someone who was suffering who was presented to him".
Fuelling the speculation is Francis' obsession with Satan, a frequent subject of his homilies. In his very first homily as pope, on March 14, Francis warned cardinals gathered in the Sistine Chapel the day after he was elected that "he who doesn't pray to the Lord prays to the devil".
He has since mentioned the devil on a handful of occasions, most recently in a May 4 homily when, in his morning Mass in the Vatican hotel chapel, he spoke of the need for dialogue — except with Satan.
"With the prince of this world you can't have dialogue: let this be clear!" he warned.
Experts said Francis' frequent invocation of the devil is a reflection both of his Jesuit spirituality, his Latin American roots — and a reflection of a Catholic Church weakened by secularisation.
"The devil's influence and presence in the world seems to fluctuate in quantity inversely proportionate to the presence of Christian faith," said Reverend Robert Gahl, a theologian at Rome's Pontifical Holy Cross University.
"So, one would expect an upswing in his malicious activity in the wake of de-Christianisation and secularisation" and a surge in things like drug use, pornography and superstition.
In recent years, Rome's pontifical universities have hosted several courses for would-be exorcists on the rite.
While belief in the devil is consistent with church teaching, the Holy See does urge prudence, particularly to ensure that the afflicted person is not merely psychologically ill.
Reverend Giulio Maspero, a Rome-based systematic theologian who has witnessed or participated in more than a dozen exorcisms, says he is certain that Francis' prayer on Sunday was either a full-fledged exorcism or a prayer to "liberate" the young man from a demonic possession. He noted that the placement of the pope's hands on the man's head was the "typical position" for an exorcist to use.
"When you witness something like that — for me it was shocking — I could feel the power of prayer," he said, speaking of his own experiences.
Maspero said it was particularly symbolic that Francis' purported exorcism occurred on Pentecost, an important feast day for the church, when the faithful believe Jesus' apostles received the fullness of the Holy Spirit.
"The Holy Spirit is connected to the exorcism because ... it is the manifestation of how God is present among us and in our world," he said.
While the Vatican spokesman, Reverend Federico Lombardi, sought to dampen suggestions that what occurred was a full-fledged exorcism, he did not deny it, saying Francis had not "intended" to perform one.
Italian newspapers noted that the late Pope John Paul II performed an exorcism in 1982 close to the same spot where Francis prayed over the young disabled man on Sunday.