On Thursday, Indian Foreign Minister Sushma Swaraj told the General Assembly that India remained open to dialogue, "but talks and terror cannot go together."
"We don't need four points, we need just one: Give up terrorism and let us sit down and talk," she said.
Swaraj said the talks between national security advisers on all issues related to terrorism should be held, as well as an early meeting of senior military officials to address the situation on the border.
"If the response is serious and credible, India is prepared to address all outstanding issues through a bilateral dialogue," she said.
Planned talks between national security advisers from India and Pakistan were cancelled in August hours before they were due to start, dashing hopes the two might tackle the violence that many fear could one day spark a nuclear showdown.
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In the talks, India had wanted only to discuss terrorism-related issues. Pakistan sought a wider agenda, including the status of Kashmir.
India and Pakistan have fought three wars since becoming independent countries in 1947, two of them over the Himalayan region of Kashmir, which both claim in full but rule in part.
Sharif, elected in 2013, promised to improve relations with India. But since then domestic troubles have forced him to cede more control over foreign and security policy to Pakistan's more hawkish military.
Indian Prime Minister Narendra Modi has taken a hard line with Pakistan, insisting he is unwilling to discuss other issues unless Pakistan admits its role in terror attacks in India.
India's Ministry of External Affairs made it clear that Sharif's proposal was a non-starter. "To de-militarize Kashmir is not the answer," ministry spokesman Vikas Swarup said in a tweet. "To de-terrorize Pakistan is."