Napolitano, who is not accused of playing a role in the alleged deal, gave evidence Tuesday as prosecutors attempt to unearth fresh evidence on mob bombings two decades ago which killed 21 people including two top anti-Mafia judges.
According to a transcript of the hearing released by the president's office, he told prosecutor Nino Di Matteo the attacks were a form of "extortion or outright pressure aimed at destabilizing the entire system, on the premise that there there might be disarray among state authorities".
High-ranking ministers are suspected of having negotiated with the Sicilian Mafia to end the violence which shook Florence, Milan and Rome in exchange for softer jail sentences and better conditions in prison for convicted mobsters.
The bombings "followed one another according to a direct and persistent logic, to give the public powers an ultimatum so that they (the Mob) could suggest the easing of prison sentences and conditions for Mafia members as a way out," Napolitano said.
The 89-year-old, former head of the lower house of parliament, denied knowing anything about the alleged deal between the state and the Mafia.
The trial being held in Palermo moved to the presidential palace in Rome to hear Napolitano's testimony, which was given behind closed doors.
Napolitano also said then prime minister Carlo Azeglio Ciampi had feared a coup was imminent, particularly after a blackout in the premier's offices in April 1993 in what he described as a "classic" pre-coup move.
The six mob-connected figures prosecutors have in their sights include Mafia chief Toto "The Beast" Riina.
The case is likely to drag on for years. The trial is not expected to reach a verdict before the end of 2015, and under the Italian legal system it can then be appealed twice before the verdict becomes conclusive.