The Taliban had said Mastrogiacomo, who was picked up on Monday in southern Afghanistan's Helmand province with two Afghan colleagues, had confessed to spying for British troops.
Khan said the Taliban had recovered a video camera, a satellite phone and "lasers in shampoo bottles" that he said could help guide air strikes to Taliban positions.
"We're investigating if the journalist Daniele was involved in bringing lasers in shampoo bottles," he said.
Mastrogiacomo works for La Repubblica newspaper, which has denied the Italian was a spy and said the Karachi-born journalist had been writing for them since 1980 and had reported from Afghanistan since February 28.
On Thursday, the Italian government demanded the Taliban provide proof that Mastrogiacomo was still alive, as hundreds of protesters gathered in Rome demanding his release.
Friends, relatives and colleagues gathered outside Rome's city hall to call for Mastrogiacomo's immediate release, saying it was impossible that he would have confessed to being a spy.
Elisabetta Belloni, head of the foreign ministry's crisis unit which handles hostage negotiations, said the government had not received any proof Mastrogiacomo was alive, needed before any talks could get under way for his release.