Tillerson has said USA aid may be cut if Pakistan does not act more proactively against the groups, and Islamabad is jeopardizing Pakistan's future by not pushing out militant groups that range across the border into Afghanistan.
The third round of talks was held in Islamabad when an interagency USA delegation visited the Pakistani capital with details of the new United States strategy for South Asia announced by President Donald Trump on Aug 21.
In September, India worked with Afghanistan and identified priorities and projects where Kabul needed New Delhi's assistance.
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After Tillerson's meeting with Ghani on Monday, the American Embassy and Ghani's office released a statement claiming that the two men had met in Kabul.
Pakistan has repeatedly denied the charge, insisting it maintains contacts only to try to bring the militants to peace talks.
"Pakistan needs to, I think, take a clear-eyed view of the situation that they're confronted with in terms of the number of terrorist organizations that find safe haven inside of Pakistan", Tillerson said after concluding the talks.
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On Tuesday, Tillerson told Abbasi that Pakistan was "so important" to regional security as the pair shook hands ahead of the meeting. "And we are looking forward to moving ahead with the U.S. and building a tremendous relationship", Abbasi replied, according to a pool report. Last month, an unannounced visit to Afghanistan by Defense Secretary James Mattis was marked by a rocket attack on the airport in Kabul.
According to the Ministry of External Affairs, Mr. Modi and Mr. Ghani spoke about India's security support as a strategic partner, including the training of Afghan personnel at Indian military academies.
US Secretary of State Rex Tillerson will arrive here on Tuesday on a three-day maiden official visit to India, during which he will call on Prime Minister Narendra Modi and meet External Affairs Minister Sushma Swaraj.
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An image released by the State Department of the same meeting featured several details, including a clock and fire alarm, that had been removed from the Afghan image.