Kashmiri moderates have welcomed the proposals
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India has asked Pakistan to discuss Kashmir through official channels only after its leader unveiled radical ideas to end years of conflict in the region.
President Pervez Musharraf made an appeal for new thinking to end the two countries' dispute over the divided territory by peaceful means.
Pakistani opposition parties reacted angrily but politicians within Kashmir itself welcomed the call.
India suggested reporters should not be first to hear new proposals on Kashmir.
"We do not believe that Jammu and Kashmir is a subject on which discussions can be held through the media," said foreign ministry spokesman Navtej Sarna.
The territory was, he added, just "one of the subjects" in the negotiations between India and Pakistan which began this January.
BBC News Online's Sanjoy Majumder, in Delhi, says Indian officials believe President Musharraf likes to score political points in public but is unyielding in his negotiations in private.
Among the options the Pakistani leader suggested were joint rule over the territory or its re-division.
He also said Pakistan's traditional demand for a referendum was impractical while India's bid to create a permanent border between the two parts of Kashmir was unacceptable.
'U-turn'
The BBC's Zaffar Abbas, in Islamabad, says the president's bold new initiative took the whole of Pakistan by surprise.
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HAVE YOUR SAY
This is the boldest step taken by any leader in South Asia
Khurram Khan, Charlotte, NC, USA
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An alliance of six Islamic parties, Muttahida Majlis-e-Amal (MMA), called the plan a "betrayal of the Kashmir cause".
"It's a U-turn, a roll-back of Pakistan's policy on Kashmir since independence," MMA deputy leader Hafiz Hussain Ahmed told AFP news agency.
"Whatever the ideas, he should have put them forward in parliament."
Raja Zafarul Haq, a senior leader of the opposition Alliance for the Restoration of Democracy, said Mr Musharraf's proposals were "not in the interest of Pakistan and the Kashmiris".
Kashmiris react
In the Pakistani-administered part of Kashmir, Prime Minister Sardar
Sikandar Hayat said he was disappointed by the president's comments on a referendum and also a suggestion that it could be divided over again.
"We believe in a plebiscite, the one which was promised to us by both Pakistan and India," he said, referring to a 1948 UN Security Council resolution calling for a referendum which was accepted by both states.
"Now, after five decades, they are talking about disintegration of Kashmir into six, seven parts."
In the Indian part of Kashmir, the leader of a hardline faction of the separatist All Party Hurriyat Conference, Syed Ali Shah Geelani, said his supporters stood by their demand for self-determination.
However, the leader of a moderate faction of Hurriyat welcomed President Musharraf's proposals.
Abdul Gani Bhat said they would be acceptable to India, Pakistan and the Kashmiris alike, and could usher in lasting peace and an era of prosperity.
Radical plan
Our correspondent in Islamabad says the intense debate is exactly what President Musharraf would have hoped for when he unveiled his radical proposals.
Speaking on Monday, the president said himself that he had "never spoken like this before to anyone".
"If both sides continue to stick to their stands, the dispute would persist for 100 years without any solution," he added.
India and Pakistan have fought two of their three wars since independence over Kashmir, since when they have both acquired nuclear arsenals.