In a meeting with a group of reporters and TV anchorpersons in Islamabad, Prime Minister Khan said that he had received a letter from President Trump on Monday.
The U.S. embassy in Islamabad had no immediate comment on the letter.
Asserting that 40 years is enough for every responsible nation to get on board with the south Asia peace process, US Defence Secretary Jim Mattis, in a strong message to Pakistan, said it is time for everyone to support the efforts of the UN, Prime Minister Narendra Modi and Afghanistan in this regard.
Trump told Khan the Pakistan relationship was very important to the USA and to finding a solution to the Afghanistan conflict, Chaudhry added.
The letter was a damning indictment that Pakistan is yet to act to deal with the Taliban.
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The U.S. and Afghanistan have long accused Pakistan of turning a blind eye to the Afghan Taliban, whose leadership is based in Pakistan.
President Trump reiterated those allegations in a television interview and subsequent tweets last month, justifying his suspension of military assistance to Pakistan.
Prime Minister Khan had led the sharp reaction by political leaders to Trump's tirade against Pakistan by hinting at review of foreign policy options and asking the U.S. president to introspect on the real reasons for America's failure in Afghanistan. Trump wants to end a 17-year-old war between Afghan security forces and the Afghan Taliban militants, who are fighting to drive out global forces and establish their version of strict Islamic law.
Opposition leaders expressed their reservations over Prime Minister Imran Khan's statement hinting towards the possibility of early elections in the country, terming it "irresponsible" as they criticised his government's performance in the first 100 days of power.
Officially allies in fighting terrorism, Pakistan and the United States have a complicated relationship, bound by Washington's dependence on Pakistan to supply its troops in Afghanistan but plagued by accusations Islamabad is playing a double game.
At an global conference on Afghanistan in Geneva last Monday, Afghan president Ashraf Ghani said a 12-person Afghan negotiating team has been prepared for peace talks.