"I had read about some new ideas and thoughts expressed from Pakistan," Singh said during a speech in the northern Indian city of Amristar.
"We welcome all ideas as they contribute to the ongoing thought process," he said in Punjabi, according to the official English text of the speech. "The destinies of our two nations are interlinked. We need to put the past behind us."
Still, the spokeswoman for Pakistan's foreign ministry, Tasnim Aslam, said of Singh's speech, "they are positive comments."
Split between overwhelmingly Hindu India and Muslim Pakistan, Kashmir is claimed by both countries, which have fought two of their three wars over the predominantly Muslim region since independence from Britain in 1947 during the bloody partition of the subcontinent.
Pakistani President Gen. Pervez Musharraf earlier this month said Islamabad was willing to give up its claim to all of Kashmir if India reciprocated and agreed to jointly administer the region, which would be granted a wide degree of autonomy.
While Musharraf has made similar suggestions before, the comments in an interview with India's NDTV news channel were among his strongest to date.
Musharraf's comments also came just weeks after India and Pakistan renewed their peace process, temporarily suspended by New Delhi following the July 11 Mumbai train bombings, which killed more than 200 people. India says Pakistan's intelligence agency played a role in the attack, a charge Islamabad denies.
India has in the past been irked by Musharraf making peace overtures through the media, and Singh's comments show that "this time around, they are saying 'come, show us the proposal, let's talk,"' said Samina Ahmed, the South Asia project director for the International Crisis Group, a think tank.
"What's really important is for the two sides to keep talking, it doesn't help when the dialogue breaks down," she said in a telephone interview from Islamabad. But, Ahmed cautioned: "this is a long and painful process. it's not going to be resolved overnight."
Begun in 2004, the peace process between the longtime rivals, both nuclear-armed, has seen tensions ease considerably in South Asia.
But Kashmir has remained the main sticking point.
India has repeatedly demanded that before any moves are made to end the dispute over the region, Pakistan must clamp down on Islamic militants fighting Indian rule in Kashmir, an insurgency that has killed about 68,000 people since its onset in 1989.
New Delhi accuses Pakistan of providing training and material to the insurgents, while Islamabad says it only provides diplomatic and moral support.
Although there has been scant public progress in settling the Kashmir dispute, officials on both sides privately say advances have been made in back channel negotiations, largely between retired officials on both sides.
The officials, speaking on condition of anonymity because of the sensitivity of the talks, have said the main features of a Kashmir deal would be an opening for travel and trade of the heavily fortified frontier between the Indian- and Pakistani-controlled parts of Kashmir. There would also be a staggered withdrawal of troops from each side of the region.
Accepting such a plan would be a major departure for both Pakistan and India.
Islamabad has previously insisted a referendum be held in all of Kashmir to determine whether the region should be part of India or Pakistan.
New Delhi, meanwhile, says Kashmir is an integral part of India and has resisted moves to redraw its borders.
Indian External Affairs Minister Pranab Mukherjee is scheduled to visit Islamabad for talks on Jan. 13, and India's prime minister is expected to visit Pakistan sometime early next year.