Pakistan has accused India's prime minister of distorting remarks made by its President, Pervez Musharraf, at the United Nations.
Mr Vajpayee: No talks with terrorists
On Thursday, Indian PM Atal Behari Vajpayee accused Pakistan of "terrorist blackmail" in the dispute over Kashmir during a speech at the UN general assembly.
He said President Pervez Musharraf's offer of a ceasefire was tantamount to admitting that Islamabad sponsored militants fighting Indian rule there.
The heated rhetoric from both sides is being as a fresh blow to peace prospects between the two nuclear rivals.
In his speech Mr Vajpayee repeated India's line that it would only hold talks with Pakistan when "cross-border terrorism" had ended.
Islamabad said it was disappointed with Delhi's response.
"By rejecting the president's constructive proposal for dialogue and diplomacy, India has spurned peace," foreign office spokesman Masood Khan told the BBC.
Mr Vajpayee's speech was greeted in the Indian press on Friday as a fitting reply to General Musharraf's earlier one.
Indian forces have been fighting Kashmir militants for over a decade
"Prime Minister Atal Behari Vajpayee's speech was a sophisticated decimation of Pakistan President Pervez Musharraf's Kashmir posturing, with Mr Vajpayee declaring India's refusal to 'let terrorism become a tool of blackmail'," The Pioneer said.
In a front-page lead headlined "PM blows chill wind over Gen's hot air", The Indian Express said Mr Vajpayee had rebutted the general's comments on the Kashmiri separatist movement by pointing out that the people of the state had taken part in democratic elections last year.
"The reference to democracy in India," the Express says, "even as Musharraf steadfastly refuses to get out of his uniform, was intended to remind the Security Council and especially the US, that India's struggle to move ahead was taking place within such parameters."
But a note of caution was sounded by The Times of India.
"The tone of exchanges during the torrid week in New York now appears to have put even more distance between India and Pakistan after a brief period of hope," The Times warns.
The Pakistani media has taken a different view of Mr Vajpayee's remarks, seeing it as an opportunity lost.
They said that the prime minister would have done well to consider President Musharraf's offer to enlarge the UN observer mission along the line of control.
"India has repeatedly refused to talk to Pakistan by alleging that Islamabad-aided 'cross-border terrorism' stand in the way of dialogue," writes The Dawn.
Musharraf called for a complete ceasefire in Kashmir
"What better way to establish the truth or otherwise?"
The News adds that India stood to lose nothing in joining forces with Pakistan to solve the long-running Ksahmir dispute.
"There is no prize involved in following a path of no-cooperation as to let issues remain unresolved," it said.
General Musharraf had accused India of refusing to enter a dialogue over Kashmir, which he called the world's most dangerous dispute - a reference to the nuclear weapons both countries possess.
He called for a complete ceasefire along the Line of Control which divides the disputed Himalayan territory.
India accuses Pakistan of arming, training and funding the rebels.
Pakistan says it provides only moral and diplomatic support to "freedom fighters", and accuses India of gross human rights abuses in Kashmir.