Trump has repeatedly accused Pakistan of failing to crack down on Islamic militants operating along the border and last month said it had harbored Osama bin Laden for years despite getting billions of dollars in American aid.
Pakistan's Foreign Ministry did not release the letter, but said it expressed Trump's commitment to achieving a negotiated settlement to the war in Afghanistan. The ministry said the letter suggested the two countries "explore opportunities to work together and renew their partnership."
Pakistan's Information Minister Fawad Chaudhry said Khan received the letter Monday morning. The ministry welcomed the U.S. president's outreach, saying "Pakistan has always advocated a political settlement to end war in Afghanistan."
"Pakistan reiterates its commitment to play the role of facilitator in good faith," the ministry said. "Peace and stability in Afghanistan remains a shared responsibility." In comments broadcast on state-run television, Khan said "peace in Afghanistan is in our own interest."
"We will try our best to bring the Afghan Taliban to the negotiating table with America," he said. The U.S. and Afghanistan have long accused Pakistan of turning a blind eye to the Afghan Taliban, whose leadership is based in Pakistan. Islamabad has always denied the allegations, pointing to its efforts to combat homegrown extremists who have carried out hundreds of attacks inside Pakistan.
Pakistan also angrily rejected Trump's comments on bin Laden, saying such "baseless rhetoric" was "totally unacceptable." Bin Laden was killed by U.S. commandos in a surprise raid in May 2011 in the Pakistani garrison city of Abbottabad. Pakistan has always denied knowing he was there.
Imtiaz Gul, a Pakistani analyst, said Trump's letter indicates there is a realization within the U.S. administration that Pakistan's cooperation is vital to ensuring peace in Afghanistan. Despite near-daily attacks by the Taliban, who now hold sway in about half of Afghanistan's territory, the Trump administration has stepped up efforts to find a peaceful solution to the protracted war.
U.S. envoy Zalmay Khalilzad was expected in Pakistan this week during his visit to the region to revive peace talks with the Taliban. The State Department said he will travel to Pakistan, Afghanistan, Russia, Uzbekistan, Turkmenistan, Belgium, the United Arab Emirates and Qatar this month.