The talks in New Delhi are the first Singh will hold with leaders of the All Parties Hurriyat Conference - an umbrella grouping of moderate Kashmiri religious and political groups - since his Congress party formed the government last year.
The separatist groups have been demanding Kashmir's independence from India or its merger with neighbouring Pakistan for more than five decades.
The campaign turned violent in 1989 with more than a dozen groups fighting security forces in the Indian-controlled portion of the region.
The nearly 16-year separatist war has killed more than 66,000 people, most of them civilians.
Two rounds of talks between India's previous Vajpayee government and Hurriyat leaders made scant progress.
India has rejected Hurriyat demands that it be included in talks between India and Pakistan on resolving their rival claims to Kashmir.
While New Delhi is highly unlikely to grant independence to Kashmir, smaller steps, including a reduction in its military presence and a greater level of local administration, are possible.
"We hope it's going to be a new beginning," Umar Farooq, leader of the Hurriyat delegation, told independent New Delhi Television on Monday.
The Hurriyat was likely to press for a reduction in the army presence in Kashmir and for a release of political prisoners during Monday's talks, scheduled to take place in the evening.
Umar Farooq says a political, not
military approach is needed
"The Kashmir problem has to have a political approach. We can't carry on with a military approach," Farooq said.
The Kashmiri leader said the Hurriyat would adopt a "step by step" approach at the talks.
"Let's go slow, but let's have some concrete progress on the ground," he said.
Singh's talks with the Kashmiri separatists are being held ahead of a planned meeting on 14 September between the Indian prime minister and Pakistani President General Pervez Musharraf in New York on the sidelines of the UN General Assembly.
Police said three brothers were shot dead at point-blank range in the southern district of Doda early on Monday, adding that two of them were policemen working with counter-insurgency forces.
Tens of thousands of people have
died in Kashmir since 1989
In the same district, police said suspected separatists shot dead a Muslim girl, while a middle-aged Muslim woman had her throat slit in the neighbouring district of Poonch late on Sunday, also by suspected separatists.
None of the dozen groups active in Indian Kashmir has claimed responsibility for the killings.
Sixteen people including two women were injured in a grenade attack by suspected Islamic fighters near a busy southern town on Monday, a police spokesman said.
He said the grenade missed an army patrol and exploded among pedestrians near the town of Shopian, 50km south of Srinagar. There were no army casualties.
Indian and Pakistani officials have met several times since they began a peace dialogue in January 2004, with the latest round of talks in Islamabad last week.
The talks covered steps the two nuclear-armed neighbours could take to restore confidence, maintain peace along their border and resolve their dispute over Kashmir.
Hostility over Kashmir began soon after India and Pakistan became independent in 1947.
Both claim the region in its entirety, and have fought two of their three wars over the region.
India accuses Pakistan of fomenting the unrest in Kashmir by funding and training the separatists, a charge Islamabad denies.
Pakistan says it only offers them diplomatic and moral support.