The conversation followed Tuesday's prisoner swap that won freedom for American Kevin King and Australian Timothy John Weeks, the two university professors who had been held hostage by the Afghan Taliban since August 2016. In return, the Afghan government freed three high-ranking Taliban prisoners.
Khan "re-affirmed" Pakistan's commitment to help advance the Afghan peace and reconciliation process to promote a political settlement to the conflict in the neighboring country, a statement said. "Both leaders agreed to continue to work together for the promotion of this shared objective," it added.
King and Weeks were teaching at Kabul's American University of Afghanistan before they were kidnapped at gunpoint in the Afghan capital.
Pakistani officials have maintained, without elaborating, that they have played a role in facilitating the prisoner swap as part of their ongoing efforts to promote peace in Afghanistan.
Taliban leaders allegedly shelter and use Pakistani soil for directing insurgent activities on the Afghan side of the largely porous border between the two countries. Islamabad denies the allegations but does not rule out the possibility of insurgents taking shelter in areas across Pakistan that still host about 3 million Afghan refugees.
Trump also spoke to Afghan President Ashraf Ghani to thank him for his cooperation in the release of the two professors. Additionally, Trump invited the Afghan leader for an official visit to the U.S., which Ghani accepted, according to an Afghan presidential spokesperson in Kabul, while releasing details of the conversations between the two leaders.
Thursday's statement from Pakistan noted Khan also kept Trump apprised of the current situation stemming from India's recent controversial actions in the Indian-administered part of the disputed Kashmir region. He "stressed that the [U.S.] president must continue his efforts for facilitation of a peaceful solution" of the territorial dispute. Pakistan also administers a portion of the Himalayan region.
In August, New Delhi unilaterally ended a special constitutional autonomy for Kashmir and bifurcated it into two union territories. The move accompanied curfew-like restrictions and a communications blockade in Kashmir in addition to the detention of hundreds of people, including prominent political figures. Indian officials claim the situation is returning to normalcy as restrictions are being eased. Indian political opposition figures and residents in Kashmir reject those claims.
Pakistan condemned the actions and swiftly downgraded diplomatic and trade ties with India, saying Kashmir has been recognized as a disputed territory by the United Nations, and that neither country can alter its status.
New Delhi defends its actions in Kashmir as an "internal matter," saying they are aimed at bringing economic prosperity and development to the violence-torn region.