The Pakistani media reported that Afghan President Ashraf Ghani telephoned Prime Minister Imran Khan to discuss the ongoing worldwide efforts for peace and reconciliation in Afghanistan.
Mr Graham also claimed that the prime minister had endorsed the Trump administration's plans that the United States should keep its presence in Afghanistan and continue the reconciliation process.
"I've seen things change here and all in a positive direction", Graham, a member of the Senate Armed Services Committee who has generally been a staunch supporter of Trump, told the news conference. Once the foreign forces leave Afghanistan, sustainable peace in the region will rely on Afghanistan's relations with its neighbors.
Trump would be "far more enthusiastic about the region than he is today" if he met Khan, said Graham, who held talks with the prime minister earlier on Sunday.
Senator Lindsey Graham called on Foreign Minister Shah Mahmood Qureshi at the Foreign Office in Islamabad on Sunday.
Relations between erstwhile allies Pakistan and the United States have been tense since Trump cut more than $1bn in U.S. security assistance to the country past year, accusing the government of duplicity in its dealings with Afghanistan.
However, US officials accused Pakistan several times for turning the blind eye to or even making collaborations with the Afghan Taliban.
Pakistani Prime Minister Imran Khan (R) speaks with USA special envoy Zalmay Khalilzad (3rd L) during a meeting at the Prime Minister's office in Islamabad, Pakistan, in this handout photo released January 18, 2018.
Pakistani leaders say they support for a peace process, which has suffered a setback because of the Taliban's persistent refusal to directly talk to the Afghan government in Kabul.
Khan has been equally critical of Trump, saying before 2018's election in Pakistan that a potential meeting with the U.S. president would be a "bitter pill" to swallow.
Relations between Pakistan and the United States of America are 'gradually improving, ' says foreign minister.
Responding to a question about the actual objective of his visit, Senator Graham said: "I did not come here to negotiate with Taliban but to see a new opening for reconciliation in Afghanistan which I'd never seen before".
However, Washington hopes that Pakistan can help end the conflict. However, the aim is to enhance the US Afghanistan efforts for peace.
He termed it a "big change" as besides military efforts the government of Pakistan was also trying to economically develop tribal areas to overcome militancy there. Fired up by the commitment of making sure that Afghanistan is not consumed by terrorism after the USA pull-out, he is meeting all the stakeholders in Pakistan and has kept his tour open-ended.
"The world's not going to let the Taliban take Afghanistan over by force of arms".
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