At a function overnight marking the 61st anniversary of the creation of Pakistan, Musharraf said that political stability was needed to fight extremism and boost the nuclear-armed nation's economy.
"It's my appeal that we should adopt a reconciliatory approach so that stability should return," a grim-faced Musharraf told the gathering at the presidential palace in Islamabad.
It was Musharraf's first public appearance since the ruling coalition announced plans one week earlier to impeach him. It is the only time that a president has faced such a move in Pakistan's history.
But Nawaz Sharif - who was ousted by Musharraf in a military coup in 1999 and is now leader of the second biggest party in the ruling coalition -- said the president had to go.
"There is no safe passage for him now," Sharif told a cheering crowd in the eastern city of Lahore, referring to suggestions that Musharraf could be allowed to go into exile to avoid possible criminal charges.
"He wants safe passage after breaking the law. He wants safe passage after violating the constitution. He wants safe passage after bargaining our sovereignty," he said.
Prime Minister Yousuf Raza Gilani meanwhile called for "a policy of reconciliation" -- but made it clear that it did not apply to Musharraf.
"The period of oppression is over forever. Dictatorship has become a story of the past," Gilani said in a speech after the traditional hoisting of the national flag in Islamabad.
The Pakistan People's Party of slain former premier Benazir Bhutto, the most powerful party in the ruling coalition, said that impeachment charges against Musharraf had almost been finalised.
"I am pleased to announce on independence day that the impeachment process is moving fast and is on the right track," party spokesman Farhatullah Babar said, adding that consultations on the impeachment charges would continue Thursday.
The coalition needs a two-thirds majority in a combined sitting of the upper and lower houses to topple Musharraf but has been putting pressure on him to quit before the impeachment process starts.
Local newspaper reports quoted the party as saying that the impeachment motion would be lodged on Monday.
Three of Pakistan's provincial assemblies have this week approved no-confidence motions in Musharraf and the fourth and final is due to do so on Friday.
With the issue heightening instability, the run-up to Independence Day was marred when a suicide bomber blew himself up in a crowd of policemen in Lahore on Wednesday night, killing eight people.
Officials said the attack was likely revenge for Pakistani military operations in the troubled tribal belt bordering Afghanistan that have killed more than 180 people in the past week.
Fighting in the Bajaur tribal zone, a known haunt of Al-Qaeda and Taliban militants, continued on Thursday and Islamabad is under intense US pressure to stop militants launching attacks in Afghanistan.
Pakistan also faces economic problems including record inflation, growing unemployment, massive electricity shortages and a plummeting stock market.