By Michelle Nichols

UNITED NATIONS (Reuters) - India began a campaign to isolate Pakistan at the United Nations on Monday, telling the 193-member General Assembly it was time to identify nations who nurture, peddle and export terrorism and isolate them if they don't join the global fight.

India's External Affairs Minister Sushma Swaraj said the arrest of Pakistani Bahadur Ali was "living proof of Pakistan's complicity in crossborder terror." India has said Ali confessed that he was trained by the Lashkar-e-Taiba (LeT) militant group.

"But when confronted with such evidence, Pakistan remains in denial. It persists in the belief that such attacks will enable it to obtain the territory it covets," she said on the final day of the annual gathering of world leaders at the United Nations.

"My firm advice to Pakistan is: abandon this dream. Let me state unequivocally that Jammu and Kashmir is an integral part of India and will always remain so," Swaraj said.

India accuses Pakistan of having a role in a Sept. 18 raid on an Indian army base in Kashmir, one of the deadliest attacks in the Himalayan region that has been divided since 1947 and lies at the heart of the nuclear-armed neighbors' rivalry. Pakistan denies any role in the attack.

"We need to forget our prejudices and join hands together to script an effective strategy against terror," Swaraj said. "And if any nation refuses to join this global strategy, then we must isolate it."

India's Prime Minister Narendra Modi vowed on Saturday to mount a global campaign to isolate Pakistan. Last month U.S. Secretary of State John Kerry urged Pakistan to join other nations in fighting terrorism.

India has long accused Pakistan of backing militant groups operating in disputed Kashmir as well as of sending fighters to other parts of the country to carry out acts of violence. Pakistan denies the allegations.

Pakistani Prime Minister Nawaz Sharif last week told the U.N. General Assembly India had put unacceptable conditions on dialogue.

"What pre-conditions?" Swaraj said on Monday. "We took the initiative to resolve issues not on the basis of conditions, but on the basis of friendship."

Pakistan's U.N. Ambassador Maleeha Lodhi dismissed Swaraj's statement on Monday as "a litany of falsehoods and baseless allegations."

"For the Indian Foreign Minister to claim that her country has imposed no preconditions for talks with Pakistan is another flight from reality. India suspended talks more than a year ago, and has refused to resume these despite repeated offers from Pakistan," Lodhi said.

(Reporting by Michelle Nichols; Editing by David Gregorio)