Sharif, seen as the biggest challenge to Musharraf since last week's assassination of Benazir Bhutto, said the former military chief who took power after a bloodless coup in 1999, should quit right away, The New York Times reported.
Sharif, who was sent into exile after his downfall, returned earlier this year to contest in the elections set for next week.
Attacking Musharraf, Sharif told a news conference in Lahore, "He is a one-man calamity and the source of all the problems. The country is burning."
Lahore, capital of the Punjab province, is the headquarters of Sharif's faction of the Pakistan Muslim League.
His brother, Shahbaz, also a prominent politician, said Musharraf should leave to allow a government of "national consensus" to be formed in consultation with the opposition parties.
Earlier, Nawaz Sharif's party said it would participate in the upcoming elections, reversing an earlier decision to boycott them made immediately after Bhutto's killing.
The elections were originally set for Jan. 8 but the election commission will decide Tuesday whether to postpone them.
The Times report said both Sharif's party and Bhutto's Pakistan Peoples Party, now led by her son and husband, feel they can draw much support from a public angered by the Bhutto killing.