Khan told Trump there was only one solution for Afghanistan and that a peace deal with the Taliban was closer than it had ever been. He said he hoped in the coming days to be able to urge the Taliban to continue the talks.
The United States views Pakistan's cooperation with a deal to end the 17-year-old war as essential but the two countries have a complicated relationship.
Trump wants to wrap up U.S. military involvement in Afghanistan and sees Pakistan's cooperation as crucial to any deal to end the war and ensure the country does not become a base for militant groups like Islamic State.
Washington wants Islamabad to pressure Afghanistan's Taliban into a permanent ceasefire and participation in talks with the Afghan government.
Trump last year slashed millions of dollars of security assistance to Islamabad, which it accused of serving as a safe haven for militants. Pakistan has denied the accusations.
Authorities in Pakistan last week arrested Hafiz Saeed, The Pentagon said Pakistan's army chief, General Qamar Javed Bajwa, will meet later on Monday with the top American military officer, chairman of the U.S. Joint Chiefs of Staff General Joseph Dunford. Analysts believe Bajwa will play a key role in behind-the-scenes discussions in which much of the serious business of the visit will take place, with the military looking to persuade Washington to restore aid and cooperation.