“For progress to be made, it is imperative that the territory of Pakistan and the areas under its control are not utilised for aiding or abetting terrorism,” Singh said.

“It is equally important that the terrorist machinery that draws its sustenance from Pakistan be shut down.”

Singh said he supported resolving questions over Kashmir - which is divided between the South Asian powers and is claimed by both - but stood firm that the Himalayan territory is “an integral part of India.”

“There can never, ever, be a compromise with the unity and territorial integrity of India,” he said.

A raid by militants on an Indian army base in Kashmir killed 10 people on Thursday. Jammu and Kashmir state chief minister Omar Abdullah said the attack “aimed at derailing” dialogue between India and Pakistan.

At the United Nations, Singh called for greater international cooperation against state support for extremism.

“There can be no tolerance for states sheltering, arming, training or financing terrorists,” he said.

Sharif, who in the past has cooperated with Islamist groups, has quickly sought to reassure the United States and India after sweeping to power in May with promises to rebuild Pakistan’s troubled economy.

While addressing the UN General Assembly on Friday, Sharif said he was looking for a “substantive and purposeful dialogue” with Singh to offer a chance for “a new beginning” with India.

“Our two countries have wasted massive resources in an arms race,” Sharif said. “We could have used those resources for the economic well-being of our people.”

Sharif also reiterated calls for greater international attention on Kashmir, a longstanding position of Pakistan.

Pakistan followed India in developing nuclear weapons, with late prime minister Zulfikar Ali Bhutto famously saying his country was ready to “eat grass” to have the weapons.

The presence of atomic arms has raised fears over the repercussions of conflict between India and Pakistan - caused either by a major attack inside India or an escalation of conflict over Kashmir.

While Sharif has returned to office, Singh - who turned 81 on Thursday - is seen to be on his way out. He has headed the world’s largest democracy since 2004 and is not expected to lead his Congress Party next year’s elections.

Singh, who was born in what is now Pakistan before India’s partition at independence in 1947, has supported stable relations with Pakistan but has warned that any substantive improvement in ties requires Islamabad to crack down on virulently anti-Indian Islamic militants, some of whom operate openly.

Singh resisted domestic pressure for military retaliation after a 2008 raid on a luxury hotel in Mumbai killed 166 people, but he has repeatedly urged Pakistan to prosecute extremists over the attack.

In a valedictory visit to the White House on Friday to see President Barack Obama, the Indian leader voiced weariness about his decade of dealing with Pakistan.

“The expectations have to be toned down given the terror arm which is still active in our subcontinent,” Singh told Obama of his meeting with Sharif.

A quiet diplomatic bid a decade ago to reach a comprehensive solution over Kashmir failed, but India and Pakistan have since taken goodwill steps.

Last month, Pakistan freed nearly 340 Indian fishermen who had been detained for mistakenly straying into the neighbouring country’s waters.