AFP/ Islamabad

Pakistan's Prime Minister Nawaz Sharif has proposed a new peace initiative with India centred around the demilitarisation of the disputed territory of Kashmir, where a surge in cross-border shelling has killed dozens of civilians since last year.

Speaking at the UN General Assembly on Wednesday, Sharif outlined a four-point initiative to de-escalate tensions between the two nuclear-armed countries which have fought three full-scale wars since they gained independence from Britain in 1947.

He called for the UN to expand its monitoring effort and for both countries to: respect a historic 2003 ceasefire agreement in Kashmir, renounce the "threat of use of force under any circumstance", reduce their military presence in the region, and unconditionally withdraw from the contested Siachen Glacier, the world's highest battleground.

"South Asia needs strategic stability and this requires serious dialogue to achieve nuclear restraint, conventional balance and conflict resolution," he said.

India's foreign office immediately hit back at the speech in a series of tweets from its official spokesman Vikas Swarup.

"To de-militarise Kashmir is not the answer, to de-terrorise Pakistan is," he said in one tweet. India maintains that Pakistan helps militant proxies infiltrate the territory's de facto border to foment unrest.

Indian critics also contend that peace overtures from Islamabad's civilian government are ultimately hollow because it is Pakistan's powerful army, which has ruled the country for almost half its existence, that controls foreign policy.

Sharif swept to power in 2013 pledging to normalise ties with India.

After the election of his counterpart Narendra Modi in India a year later, hopes were high that a breakthrough might be possible.

Instead a surge in firing across the de-facto Kashmir border since 2014 has claimed dozens of civilian lives on both sides and brought relations to their lowest level in more than a decade.