Singh offered to hold talks on 5 September with the main Kashmiri separatist alliance, the Hurriyat Conference, said his spokesman Sanjaya Baru on Wednesday.
The Kashmiri delegation is to be led by Mirwaiz Omar Farooq, the head of the alliance's moderate faction.
Farooq said the Hurriyat had accepted Singh's invitation. A hardline faction which favours integration of Kashmir with Pakistan has not been invited.
"We have received an invitation and, in principle, have accepted the invitation," Farooq told Reuters in Indian-administered Kashmir's summer capital Srinagar.
He said he was upbeat about the talks.
"The circle will be complete now. India is talking to Pakistan, Pakistan talks to us and we talk with India"
Mirwaiz Omar Farooq,
Kashmiri separatist leader
Government officials had been in contact with them through mediators.
The announcement came weeks after Farooq said the separatists were ready for talks and were awaiting an invitation.
""Both India and Pakistan do realise that the time has come to settle all issues, including Kashmir, in accordance with the aspirations of the people of Kashmir," Farooq told the media.
The Hurriyat's policy-making executive council will meet on
Thursday to finalise its stand at the talks, he said.
"If we can build trust and confidence, the Kashmir dispute can be resolved," said Farooq.
"The circle will be complete now. India is talking to Pakistan, Pakistan talks to us and we talk with India," he said.
Kashmir is "a complicated issue, but it can be resolved if there is sincerity and commitment of all parties involved", he said.
Farooq (R) will lead the Kashmiri
India's previous government held two rounds of talks with the Kashmiris in 2004, although little progress was made before that government lost elections later that year to Singh's Congress party.
An agreement with the separatists is crucial to pushing forward the peace process between India and Pakistan, rivals who have fought two of their three wars over Kashmir since independence from Britain in 1947.
Kashmir, the only Muslim majority state in predominantly Hindu India, is split between the two countries but claimed by both.
Since partition with Pakistan in 1947, Muslim separatists have been pushing for the region's independence.
The campaign turned violent in 1989. Some of the separatist fighters want to merge Indian-administered Kashmir with Pakistan, others want an independent Kashmir.