The spokesman, Fawad Chaudhry, says Khan received Trump's letter on Monday morning.
Pakistani media outlets, whose reporters met with Khan, quoted him as saying Pakistan would continue its efforts to help peace in Afghanistan, AP reported.
Trump's letter comes two weeks after he accused Islamabad in a tweet of harboring al-Qaeda leader Osama bin Laden despite getting billions of dollars in American aid.
At the time, Islamabad said "such baseless rhetoric ... was totally unacceptable." Khan stressed the United States had provided what he described as a minuscule $20 billion in aid to Pakistan.