Singh (left) will host a dinner for Musharraf
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Pakistan still controls "the flow of terror" into Indian-administered Kashmir, Indian premier Manmohan Singh has told US President George W Bush.
"This must stop for any real progress to be made in the peace process," Mr Singh's spokesman quoted him as saying.
Pakistani President Pervez Musharraf later voiced his hope that the current dialogue might lead to new era of peace and cooperation in the region.
The two men, in New York for the World Summit, are due to meet shortly.
They are expected to discuss progress achieved in recent talks at a one-to-one dinner on the sidelines of the UN summit.
In his address to the summit, Mr Musharraf said a solution to the Kashmir problem would put an end to the cycle of confrontation between the two countries.
Ending Kashmir rebel incursions has long been a key Indian demand.
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The South Asian rivals, who began peace talks last year, have fought two of their three wars since 1947 over the Himalayan territory.
On Wednesday, the Indian army said troops had killed three "infiltrators" in Poonch district of Indian-administered Kashmir, near the Line of Control.
Dinner date
Mr Singh made his remarks during a 30-minute meeting with President Bush on Tuesday night, his spokesman Sanjay Baru told India's NDTV television.
He said the Indian PM had told President Bush that he was "satisfied" with the peace process so far, however, despite the need for Pakistan to act on militants.
Gen Musharraf also met President Bush on Tuesday, and told him that a pullout of Indian troops from parts of Jammu and Kashmir would be a step in the right direction, Pakistan's state-run APP news agency reported.
Mr Singh is hosting a dinner for Gen Musharraf on Wednesday.
Both men are expected to push forward peace moves that include the future of disputed Kashmir.
More than 40,000 people have died in the insurgency in Kashmir.
'Constituency for peace'
India accuses Pakistan of training, arming and funding Islamic militancy in the region, a charge Islamabad strongly denies.
There are an estimated 400,000 Indian soldiers in Kashmir
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Pakistan admits extending "moral, political and diplomatic support" to Kashmiris seeking independence from India.
Pakistan's foreign minister urged both leaders to "seize the moment" during their talks on Wednesday.
"On both sides there is a constituency for peace," Khurshid Kasuri said.
"I don't remember such a long period of peace between India and Pakistan, or a time when the civil societies were so active."