The Indian Government and a group of Kashmiri separatists have agreed that violence must end in the troubled region at a historic first meeting.
Separatist Maulana Ansari kept an open mind in the talks
A moderate wing of the main Kashmir alliance met a team headed by hard-line home minister LK Advani in Delhi.
They will now meet Indian Prime Minister Atal Behari Vajpayee on Friday, another first.
Correspondents say there are still many obstacles to a deal over Kashmir, where thousands have died in an insurgency.
The BBC's Adam Mynott in Delhi says the meeting would not have happened without recent peace moves between India and Pakistan over the disputed territory of Kashmir.
Pakistani President Pervez Musharraf said on Thursday he was hopeful of a peaceful solution to the Kashmir dispute.
"There is a realisation that we need to address all issues including the issue of Kashmir to bring peace and harmony to the region," he said at the World Economic Forum in Davos, Switzerland.
In November, India and Pakistan, who fought two wars over Kashmir, agreed to a ceasefire along their shared border.
Earlier this month, they agreed to discuss Kashmir as part of peace talks due in February.
In a statement after the two-hour meeting, the Indian Government and the Kashmir separatists said they agreed the only way forward was "that all forms of violence at all levels should come to an end".
"The [separatist] delegation stressed that an honourable and durable solution
should be found through dialogue," it said.
"The deputy prime minister endorsed [Hurriyat's] view that the role of the gun should be replaced by the sound of politics."
During the talks Mr Advani said the security of all Kashmiris was the government's "foremost concern", as was the need to ensure against the violation of their rights.
"The meeting has proved a very good beginning," said Mr Advani.
He agreed to look at the issue of political prisoners in detention in Kashmir jails, a long-standing separatist demand.
But he said that those accused of "heinous crimes" would not be considered for release.
The five-member delegation of the moderate faction of the All Party Hurriyat Conference - the main separatist alliance - was led by its chairman, Moulana Abbas Ansari.
The next round of talks is to take place in March.
Our correspondent says the meeting does not change India's position, which is that Kashmir is very much part of India.
And some separatists outside Mr Abbas Ansari's faction, 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 hard-line 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."