Graham spoke at a news conference in Islamabad after meeting with Pakistani Prime Minister Imran Khan, who has previously faced criticism for suggesting peace talks should include the Taliban. "I think they will hit it off" if they meet as they have "similar personalities," said Graham of the proposed meeting between Trump and Khan.
Graham added that the war in Afghanistan "will end through reconciliation" but that no such talks should include the Islamic State group or al-Qaida. Graham said he would also urge Washington to reach a free trade agreement with Pakistan, a proposal which could be a game changer for Islamabad.
His comments came shortly after U.S. peace envoy Zalmay Khalilzad concluded his four-day visit to Pakistan, during which he met with Khan and the country's powerful military chief Gen. Qamer Javed Bajwa.
Khalilzad arrived in Islamabad on Thursday in effort to find a peaceful end to the conflict in Afghanistan. During his stay in Pakistan, local media reports suggested that efforts were underway to invite the Taliban for talks with a U.S. delegation in Pakistan.
"During the consultations (Pakistan and the U.S.) reaffirmed their commitment to advance the Afghan peace process," said a U.S. embassy statement. It said that during his meetings in Pakistan Khalilzad highlighted that all countries in the region will benefit from peace in Afghanistan.
Khalilzad has met several times with Taliban insurgents since his appointment in September. But the Taliban have consistently refused direct talks with Afghan President Ashraf Ghani's representatives, calling the Kabul government U.S. puppets.
The Taliban currently control nearly half of Afghanistan, and are more powerful than at any time since the 2001 U.S.-led invasion. Pakistan says it will continue using its influence with the Taliban to arrange their talks with Kabul and U.S. officials to end the conflict in Afghanistan.