Prime Minister Nawaz Sharif Sunday held his first talks with Indian Prime Minister Manmohan Singh, who has demanded the neighbor must crack down on Islamic extremists for any improvement in ties.Pakistani Prime Minister Nawaz Sharif, who has advocated an end to historic tensions with India since he swept to power in May elections, met Singh at a New York hotel on the sidelines of the UN General Assembly.In front of flags of the two nations, Singh and Sharif shook hands and made small talk before entering closed-door talks with aides.Sharif, in a speech to the UN General Assembly, Friday called for a "new beginning" with India and denounced the developing nations' years of intense military development as a waste of resources.But Singh, while welcoming overtures from Sharif, said that the proof of good intentions will be whether Pakistan curbs Islamic extremists who have attacked India.On Thursday, militants raided an army base on the Indian side of divided Kashmir, killing 10 people in an attack seen as an attempt to derail peace efforts.Singh said Saturday that Pakistan, where virulently anti-Indian groups operate virtually in the open, must no longer be "the epicenter of terrorism" in South Asia."For progress to be made, it is imperative that the territory of Pakistan and the areas under its control are not utilized for aiding or abetting terrorism," Singh said from the UN podium."It is equally important that the terrorist machinery that draws its sustenance from Pakistan be shut down," he said.Singh resisted domestic pressure for military retaliation after Pakistan-linked militants stormed an iconic hotel in India's largest city Mumbai in 2008, killing 166 people.The Indian leader instead pressed Pakistan to prosecute the hardline group Lashkar-e-Taiba and has said he has been disappointed by Islamabad's response.The 81-year-old Singh, who was born in Pakistan before the subcontinent's partition in 1947, has led India since 2004 and is unlikely to stand for another term in elections next year.The Hindu nationalist main opposition Bharatiya Janata Party has tapped as its electoral candidate Narendra Modi, who in the past has been staunchly critical of Pakistan.The meeting is the first between the two countries' leaders since Sharif won May elections. Singh met in August last year with Pakistan's then president, Asif Ali Zardari, on the sidelines of a summit in Iran of the Non-Aligned Movement.Sharif, who earlier in his career maintained relations with Islamist groups, has tried to reassure India after his election as he puts a top priority on reviving Pakistan's troubled economy.After his election, Pakistan freed nearly 340 Indian fishermen in a goodwill gesture and Sharif called for greater economic cooperation with the larger neighbor.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."The tone marked a shift from three decades ago, when late prime minister Zulfikar Ali Bhutto famously said that Pakistanis would "eat grass" if necessary to fund a nuclear program to match that of India.Sharif, despite his appeals, also reiterated Pakistani calls for greater international attention on Kashmir -- the trigger for two of the South Asian nations' three full-fledged wars.Sharif was prime minister during the mini Kargil war in 1999 when Pakistan-linked forces infiltrated remote Himalayan terrain on the Indian side of Kashmir, just months after India's then premier Atal Bihari Vajpayee traveled across the border with high hopes of reconciliation.Singh, while voicing a readiness to talk through problems on Kashmir, vowed that Indian sovereignty over the region was not open for discussion.