"It's possible that Satanic sects are behind this theft," said the Osservatorio Antiplagio's national coordinator Giovanni Panunzio.
"There are dates celebrated by Satanists that begin on 25 January and end on 1 February with the Satanic 'New Year," he said.
"This type of sacrilege typically occurs on these occasions," Panunzio said, urging parliament to enact legislation outlawing such sects.
A tube containing bloody shreds of clothing from the failed 1980 assassination attempt againt John Paull II and a small cross were stolen from the church of St Peter of the Ienca, near Aquila on Saturday.
More than 50 policemen and teams of sniffer dogs were deployed in the search across the surrounding Abruzzo region sparked by the thefts.
The relics were stolen from a sanctuary dedicated to the hugely popular pontiff, who will become a saint on 27 April together with Pope Giovanni XXIII - known as the "good pope".
The canonisation ceremony is expected to draw hundreds of thousands of pilgrims to Rome.
John Paul II, who died in 2005, loved to go on skiing holidays in the mountainous Abruzzo region and reportedly once took refuge in the St Peter of the Ienca church during a storm.