Alice Wells, the acting Assistant Secretary of State for South and Central Asian Affairs and acting Special Representative for Afghanistan and Pakistan, was set to be the first major American official to visit the country since the president's comments, but her visit has been put off by the Pakistan government "until a mutually convenient time".
The Foreign Office did not give any reason for postponing the visit.
It would be "premature" to interact with the senior US state department official at this time, they added.
In Washington, the state department confirmed Wells' trip has been postponed at the Pakistan government's "request", but it too did not provide any reason for delaying the visit.
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Wells' visit was scheduled as part of her three-nation South Asia tour. She would continue with her trip to Dhaka and Colombo, according to the state department.
Pakistan Prime Minister Shahid Khaqan Abbasi on Wednesday visited Saudi Arabia and held talks with Crown Prince Mohammad bin Salman.
News reports in Pakistan said he was accompanied by Asif on the trip and discussed the US' new Afghan strategy there.
The Pakistan-US ties received a fresh jolt on Saturday when Gen John Nicholson, the top US commander in Afghanistan, claimed in a TV interview that his country was aware of Afghan Taliban leadership's presence in Peshawar and Quetta.
Asif yesterday said the Afghan Taliban were the US and Afghanistan's problem, not Pakistan's.
He told reporters in Sialkot that Pakistan has been hosting the Afghan refugees for decades and the US "should help to repatriate them back to Afghanistan if they do not trust us.