In the interview with a private TV channel, he said Nawaz Sharif was suffering from "paranoia" and that was why he "speaks against me day and night."
"He is a compulsive liar," said the former military ruler, who had toppled Sharif's government and seized power in October 1999 in a bloodless coup and sent him into exile in 2000 for a decade.
Musharraf claimed that as prime minister, Sharif had agreed to a "sell out" on Kashmir issue during the visit in February 1999 of then Indian prime minister Atal Behari Vajpayee to Lahore.
He ridiculed Sharif for taking credit for the nuclear weapon tests conducted by Pakistan in May 1998 in a response to similar tests earlier by rival India.
"Nawaz Sharif was against conducting the tests but agreed under pressure from others," he said, without identifying who exerted the pressure.
Musharraf, who has been living in self-imposed exile since leaving Pakistan in 2008 and has formed his own political party under the name of All Pakistan Muslim League, also answered questions about the May 2 US operation that killed Osama Bin Laden on Pakistani soil.
He said it was wrong that questions raised by the operation were not answered with promptness. For three days after the incident no one from the government or the military spoke on the matter and "this silence was a wrong strategy."
Musharraf voiced skepiticism about the claim that Bin Laden had been living in the garrison town of Abbottabad for five years, saying it "does not logically appeal to me that he was there for all these years."