"I personally feel that it must be done within the tenures of Prime Minister Manmohan Singh and myself," he told a gathering of parliamentarians and journalists from South Asia, including India, on Friday.
"We have an understanding, we have harmony, we have complete understanding between ourselves. This I think is a very big difference between now and the past."
"The fleeting moments in history are not available every time; they come and go. The governments and leaders who grasp them create history," Musharraf said.
The peace opportunity has been created by a thaw in relations between the two nuclear neighbours and the growing realisation that the flashpoint dispute should be resolved peacefully.
Violence in Kashmir has claimed
more than 38,000 lives
The Himalayan state of Kashmir, divided between Pakistan and India and claimed by both in full, has caused two of three wars between the neighbours since their independence in 1947 from Britain.
Musharraf said keeping in view the sensitivities of both India and Pakistan, a solution had to be found which should be mutually acceptable to all the parties - Pakistan, India and the people of Kashmir.
The rivals launched a peace process in January 2004 when Vajpayee visited Pakistan for the 12th summit of the South Asian Association for Regional Cooperation.
Since then the two countries have restored road and air travel links and people-to-people contacts besides launching a bus service across the disputed borders in Kashmir.
Bin Laden alive
Meanwhile, Pakistani Foreign Minister Khursheed Kasuri said al-Qaida leader Osama bin Laden was alive, but that his network has been paralysed by Pakistani government forces.
Pakistan says bin Laden is alive
and on the run
Bin Laden is on the run with a small band of fighters, the minister said on Friday.
But the minister declined to say whether Pakistan had specific information on bin Laden's whereabouts.
"Osama bin Laden is alive and moving around from place to place, but not with a large group of people," Kasuri was quoted as saying in the English-language newspaper The News.
Bin Laden has been the world's most wanted fugitive since the US accused him of masterminding the September 11 attacks on Washington and New York.
Pakistan, a key ally of the United States in its war on terror, has handed over more than 700 al-Qaida suspects to US officials, including al-Qaida's former third-in-command, Khalid Shaikh Mohammed, who was arrested in March 2003 during a raid near Islamabad.
Two other alleged al-Qaida leaders, Ramzi Binalshibh and Abu Zubaydah, were also arrested in Pakistan.
Pakistan has also deployed about 70,000 troops in its tribal regions - considered possible hiding places for bin Laden - to track down suspected terrorists.