Moderate Kashmir separatists have held a meeting with India's prime minister, a day after key talks with his deputy.
The separatists and India agree an end to violence is essential
On Thursday they agreed a statement with LK Advani calling for dialogue and an end to Kashmir violence.
More than 35,000 people have died in over a decade of violence in Kashmir, claimed by both India and Pakistan since partition in 1947.
Correspondents say the main difficulty will be in persuading militants to lay down their weapons.
The separatist leaders involved in the talks with the central government do not exert influence over the militants.
Emerging out of the 45-minute meeting in Delhi, Mirwaiz Umar Farooq, one of the five separatist leaders of Kashmir's main separatist group the All Parties Hurriyat Conference, described it as a "courtesy call".
"We told Mr Vajpayee that the beginning he has made in his talks with [Pakistani President Pervez] Musharraf is a good one and that the entire leadership and people in Kashmir support the process," he said.
Earlier this month, Mr Vajpayee and General Musharraf agreed to discuss Kashmir as part of peace talks due in February.
In November, India and Pakistan, who fought two wars over Kashmir, agreed to a ceasefire along their shared border.
The Indian and Pakistani leaders are due to talk in February
In a statement after the two-hour meeting on Thursday, the Indian Government and the Kashmir separatists said they agreed the only way forward was an end to all forms of violence.
Pakistani President Pervez Musharraf, who is attending the World Economic Forum in Davos, Switzerland, expressed satisfaction at the talks.
"It's a very good beginning," he said. "We hope that the process of dialogue will continue."
He added: "The [India/Pakistan] relationship will progress only if we show sincerity and resolve and also, may I say, boldness."
The next round of talks between Delhi and the separatists will take place in March.
Some separatists outside the faction of Hurriyat chairman Maulana Abbas Ansari have declared the talks a failure.
Shabir Ahmed Shah, chairman of the moderate Democratic Freedom Party, described the dialogue as "much ado about nothing".
"We thought that the Indian Government might have changed its attitude after the Saarc (South Asian Association for Regional Co-operation) conference," he said.
"But that has not become evident after today's meeting."
Syed Ali Shah Geelani, who heads the hardline faction of the Hurriyat, said his stand had been vindicated by the meeting.
"We are fed up with talk of confidence-building, " he said.
"The real issue is the occupation of Jammu and Kashmir by Indian troops. Unless there is headway towards resolving the basic problem, addressing the incidental issues will not help."