Enzo Caruso, Messina's councillor for culture, said it was difficult to understand how thieves could have removed the works in a matter of minutes without detailed knowledge of the museum's layout.
"It's a very, very strange affair," Caruso told Reuters.
The theft on Saturday has shocked Italy and revived memories of the infamous 1969 disappearance of a masterpiece by Caravaggio from a Palermo church -- a case long associated with Sicily's Cosa Nostra mafia and never solved.
TOO FAMOUS TO SELL
Caruso said the stolen Antonello works were so famous that selling them even on the black market would be virtually impossible, raising the possibility that they could be used as bargaining chips or collateral in criminal dealings.
"The Mafia? It's possible they might try to blackmail the state itself in order to return them. These are the kinds of dynamics that ordinary people never get to see," he said.
He said another possibility was that the paintings could be used as guarantees or currency within the criminal underworld.
The thieves entered Messina's Accascina Regional Museum on Saturday evening, while the city was celebrating a religious festival that brought thousands into the streets.
The burglary only came to light some two hours later when tourists found two Antonello paintings, apparently discarded by the thieves, leaning against the museum railings.
Renato Schifani, the president of Sicily, issued a statement to say the museum's video surveillance system and alarm had been working normally, adding that an internal investigation was underway to see if any museum staff had been involved.
LOST PAINTINGS FOUND IN THE PAST
Caruso questioned how well prepared the thieves had been, pointing to the fact that two paintings had been left in the street. "Perhaps they did not anticipate how heavy they would be. These are wooden panels ... stealing them is not as easy as stealing a canvas that can be cut from its frame," he said.
He also said a professional art thief would normally take greater care handling works worth tens of millions of euros, saying no attempt had been made to protect the paintings.
Italy's crack squad of art police are heading to Messina to take on the case, just three days after helping to retrieve paintings by Pierre-Auguste Renoir, Henri Matisse and Paul Cezanne stolen earlier this year from a museum near Parma.
While the Rome-based art theft police have established a strong track record in finding missing masterpieces, Sicily is still haunted by the memory of the missing Caravaggio.
"I have the feeling the thieves may be keeping the (Antonellos) hidden while things calm down," Caruso said. "Or perhaps they immediately took the sea route," he added, noting that the museum lies close to the Strait of Messina.
"The hope is that sooner or later they reappear."
