Musharraf late on Monday called for a national debate on ways to end the dispute between Pakistan and India, with options to include independence or joint control of the Himalayan state.
He also proposed demilitarising Kashmir and placing sections of it under a United Nations mandate or under joint control.
"It is a very positive development," Mirwaiz Umar Faruq, the influential head of a main faction of the region's main separatist grouping, the All Parties Hurriyat Alliance, said.
"Demilitarising Kashmir should be a priority," he said, adding the alliance partners would meet in a day or two to discuss Musharraf's ideas.
Other separatists also reacted positively.
"It is a path-breaking statement. I welcome it," said Javed Mir, who in 1989 was instrumental in launching a resistance campaign against Indian rule in Kashmir.
"Musharraf is trying to be flexible. He is not insisting that Kashmir should become part of Pakistan. It is a welcome change," said Mir, who renounced arms in the mid-90s and joined the ranks of the separatists.
India rejects vote
Mir wants the Indian and Pakistani zones of Kashmir to be united and given independence by the two nuclear-armed countries.
Majority Muslim Kashmir has been divided between Pakistan and India since the two nations gained independence from Britain in 1947.
Kashmiri separatist leader Javed
Mir has welcomed the move
Both countries claim the Himalayan state and the dispute has been the cause of two of their three wars.
UN Security Council resolutions on Kashmir dating back more than five decades give the people of the region the choice of either joining India or Pakistan.
India has rejected UN calls for a plebiscite (referendum) in the region.
On Monday, Musharraf emphasised that as a vote was not acceptable to India, other options had to be explored.
One of Kashmir's groups, Jamiat-ul-Mujahidin, however, ridiculed Musharraf for departing from the vote demand.
No permanent border
"The Kashmir issue cannot be resolved through formulas other than the right to self-determination," a Jamiat press statement said.
Musharraf also ruled out turning the line of control (LoC), which divides Kashmir into Pakistani and Indian zones, into a permanent border - a position favoured in private by India although publicly it continues to demand full control of the region.
"I'm allergic to this and the Indians know that," he said. "A plebiscite is not acceptable to India and making the Line of Control a permanent border is not acceptable to Pakistan."
Separatists have long been opposed to converting the LoC into a border.
"I welcome Musharraf's non-acceptance of LoC as a permanent border. We (Kashmiris) will never allow that to happen," said senior separatist leader Shabbir Shah, who also supports Kashmir's independence.
Many residents say the solution
for Kashmir is independence
Shah, who has spent more than 20 years in various prisons for espousing Kashmir's secession from India, said Musharraf's suggestions could provide a solution to the dispute.
On the streets of Indian Kashmir's summer capital, Srinagar, residents hailed Musharraf's proposals.
"We want peace in Kashmir and it can only come when the dispute is resolved. Musharraf's suggestions can work wonders," said Muhammad Yusuf, a shopkeeper.
Kashmir is in the grip of a 15-year-old insurgency that has so far left tens of thousands dead and many more maimed.
"The two countries and Kashmiris should sit down and discuss Musharraf's options or even those Indians or Kashmiris might be having," said Yusuf.
The Indian government offered no immediate reaction to Musharraf's comments.