Vajpayee, in Pakistan for the first time in nearly five years, ruled out formal bilateral talks with Pakistani leaders at a South Asian summit in Islamabad starting on Sunday.
He said India was ready to discuss disputes over the mainly Muslim Himalayan region of Kashmir, cause of two wars between the neighbours since independence from Britain in 1947.
The dispute over the scenic region, which is divided between the neighbours along a tense front line, has cost tens of thousands of lives and less than two years ago raised the spectre of nuclear war.
"It is our belief and correct belief that Jammu and Kashmir is a part of India, but we are ready to talk about it openly," Vajpayee said in an interview with Pakistan Television.
"The world has been saying, 'you people get together and resolve your issue among yourselves'. This will take time."
Vajpayee's remarks to Pakistani television were made in New Delhi, but broadcast shortly after his arrival in Islamabad.
Pakistani President Pervez Musharraf said last month Pakistan was ready to set aside a 50-year insistence on a UN-backed referendum over Kashmir and explore other solutions.
Pakistan, accused by India of fomenting rebellion in Indian-controlled areas, is using the sidelines of the South Asian summit to push for mid-level talks on Kashmir.
"What I am suggesting is that foreign secretaries of the two countries meet for the first time to brush off agreements that already exist," Pakistani Foreign Minister Khurshid Mahmud Kasuri told reporters.
Kashmiri protesters at airport
tell Vajpayee to go home
"Let's do it fast," he said.
As he got off his plane in Islamabad, Vajpayee shook hands and exchanged a few words with Pakistani counterpart Mir Zafar Allah Jamali.
They clasped one hand together and turned to wave at the assembled cameramen and photographers.
It was Vajpayee's first visit to Pakistan since a summit in Lahore in February 1999.
In 2002, about a million troops were massed on the border after an attack on the Indian parliament that Delhi blamed on Pakistani-backed militants. Islamabad denied the charge.
Ties gradually warmed last year after Vajpayee announced he wanted to make a final push for peace in his lifetime.
"I think we can talk to Musharraf. Those talks can lead to some result"
Atal Behari Vajpayee
Indian Prime Minister
But the peace process appeared to be stalling until Pakistan announced a ceasefire on the frontline in Kashmir in November.
Asked how he viewed Musharraf, Vajpayee said: "I think we can talk to Musharraf. Those talks can lead to some result; that I also hope."
Vajpayee is among half a dozen South Asian leaders who began arriving in Islamabad on Saturday for the three-day summit of the South Asian Association for Regional Cooperation (SAARC).
The leaders of the seven SAARC nations, which also include Bangladesh, Bhutan, Maldives, Nepal and Sri Lanka, are expected to sign an agreement to set up a free trade area in their region which is home to 1.4 billion people, about a fifth of humanity.
Diplomats say the deal is of huge political significance and will help to boost ties between India and Pakistan.