Pakistani politicians privately regarded Vajpayee as one of the few Indian leaders they were comfortable talking to.
But with Sonia Gandhi's Congress party about to take power in New Delhi, Islamabad quickly pointed out that the desire for peace between the nuclear-armed neighbours was bigger than any single personality.
Foreign Minister Khursheed Mehmood Kasuri praised Vajpayee's role in initiating the process, then added: "I am confident this process will be carried forward by the next government of India.
"The process that has been initiated by Pakistan and India enjoys the support of the people and the political parties of both countries, including the Congress Party."
Kasuri said the change in government should not affect the timetable for a roadmap to peace agreed by the two countries. "Even if there some delay. I don't think it is going to be too long," he told a news briefing.
A senior official of the Ministry of Foreign Affairs commenting on the results of the Indian elections, said: "Pakistan desires peaceful and co-operative relations with India and looks forward to renewing the quest for promoting peace and stability in South Asia with the new government in India."
He said: "Pakistan will endeavour to seek a peaceful settlement of all outstanding issues between the two countries, including the Jammu & Kashmir dispute."
ARF DECISION HAILED: Pakistan also welcomed the decision of the ARF senior officials meeting to recommend Pakistan's admission to the regional security forum.
A senior Foreign Office official, while expressing gratitude of the government to the ARF members on Thursday, reaffirmed Pakistan's desire to continue to contribute positively towards promotion of peace, security and stability of the Asia and Pacific regions as a whole.
"Pakistan has been making efforts to promote holistic and harmonious development of the Asia and Pacific regions and supports greater inter-regional co-operation," he added.
Pakistan's membership of the ARF, he said, would provide a further avenue for promoting partnership for peace and development in this vast region.
It was Vajpayee who took the initiative last year in seeking to resurrect talks between countries which have fought three wars since independence in 1947 and came close to a fourth in 2002.
But as yet, Gandhi lacks the personal rapport Vajpayee established with Musharraf at a meeting in Islamabad in January.
However analysts say that as an Italian by birth, Gandhi would face more difficulties making concessions while carrying along hard-liners in New Delhi.
Fahmida Ashraf, a South Asia specialist at Islamabad's state-funded Institute of Strategic Studies, said the peace process would continue, although the pace could slow.
"Continuation of the peace process is not only linked with the change of government in India, but the whole international environment," she said. "The peace process we have started is supported by the international community.
Journalist and political analyst Ahmad Rashid said Musharraf would have been happier if Vajpayee was still at the other side of the table as Sonia was more of an unknown quantity.
"I think Congress will review this whole process," he said.
"Musharraf will have to be patient. The army will have to be far more patient and understanding of the situation in India."
If the process did slow down significantly, there was always the risk of stepped up militant violence in Kashmir, he said.
"Clearly the army has restricted the activities of the militants," Rashid said. "I hope this does not mean that one way the army will try to quicken the pace of the new (Indian) government will be to unleash the militants again".