In a wide-ranging interview with the top USA newspaper, the premier said he wanted a "proper relationship" with Washington.
"We believe they are not playing a fully constructive role as they should be in contributing to a political settlement in Afghanistan and in addressing the very real challenges that violence generated by the Taliban poses for the society", he said.
North Atlantic Treaty Organisation took the lead on worldwide security efforts in Afghanistan in 2003, wound down combat operations in 2014, and is now mainly training and advising Afghan forces so that they can handle the country's security needs.
In his interview, Khan expressed hope that talks with India would resume after the Lok Sabha elections due by May next year.
He said Iranian Foreign Minister Jawwad Zarif also paid a visit to Islamabad and discussed the modalities for Yemen peace process.
Khan refuted Trump's accusations saying that Pakistan had suffered far greater financial losses than it received in help from Washington, by participating in its war on terrorism. "We want government to consult us and the political figures in this respect", HPC member Qazi Mohammad Amin Waqad said. The US has satellites and drones.
The sources said that the draft of the letter would be ready next week and it would be sent to Prime Minister Khan for approval.More news: Fiat Panda scores zero stars in Euro NCAP test
"He was opposed even by some Muslims back then but today, as we see India and the deplorable condition Muslims are living there, even Quaid-e-Azam's opponents can see that the demand for Pakistan was justified", said the premier.
"Pakistan is an essential element in long-term stability in Afghanistan", McKenzie told members of the Senate Armed Services Committee Tuesday during his confirmation hearing for commander of the US Central Command (CENTCOM). "If we had stayed neutral after 9/11, I reckon we would have saved ourselves from the devastation that took place afterward", he explained, adding that by becoming the "front-line state for the U.S. in the war on terror, this country went through hell".
The comments come as Pakistan's army backed United States efforts for a political settlement with the Afghan Taliban to end 17 years of fighting.
The general also cautioned that the Afghan security forces "are not there yet and if we left precipitously right now I don't believe they would be able to successfully defend their country".
On being asked about accusations by the U.S. that Pakistan was "harbouring" Taliban leaders, Khan said: "I have never understood these accusations. If we had stayed neutral after 9/11, I reckon we would have saved ourselves from the devastation".
"I had gone on television and warned everyone that we will stand by the Supreme Court verdict", he recalled.
Trump's letter was followed by a visit from United States envoy Zalmay Khalilzad, who has said he hopes a deal can be in place before the Afghan presidential elections, set for April next year. I have asked our government to find out the status of the case.