The Republican senator and his delegation arrived in the federal capital early on Monday morning and held talks with the premier and Foreign Minister Shah Mahmood Qureshi.
Senator Graham’s visit comes in the backdrop of reports of an imminent US troops withdrawal from Afghanistan.
It is seen as part of Washington’s efforts to seek Pakistan’s support for persuading the Taliban to agree on a ceasefire.
The reports indicate the Trump administration intends to call back around 4,000 troops from the war-torn country as early as next week, which would reduce US military presence in Afghanistan to between 8,000 and 9,000 troops.
Talks between the US and the Taliban resumed a week ago but were paused again by Washington on Thursday, after an attack near a key US airbase north of Kabul.
According to a draft agreement from September, reached after years of negotiations, the Taliban would be required to commit to certain security measures, agree to talks with the Afghan government and promise a reduction of violence in exchange for a US troop withdrawal.
US President Donald Trump insisted last month on the need for a ceasefire and made a surprise visit to Bagram airbase in Afghanistan on November 28 and met Afghan President Ashraf Ghani.