"We hope to forge a good, productive working relationship with the new civilian government", said Nauert.
The issue becomes even more critical as Mike Pompeo is expected to land in Islamabad during the first week of September, during which high-level meetings will take place, including a meeting with PM Imran Khan.
Spokesperson of Pakistan's Ministry of Foreign Affairs, Dr Mohammad Faisal tweeted, "Pakistan takes exception to the factually incorrect statement issued by US State Dept on today's phone call between PM Khan and Sec Pompeo".
"They (Pakistan) are an important partner".
Downplaying the controversy, Qureshi said that the conversation between the secretary of state and the prime minister was "very good".
Washington has pressured Pakistan for years to crack down on the branches of the Taliban and the notorious Haqqani network operating in the country, both of which have been designated as terror groups by the United States.
'Crazy Rich Asians' author wanted in Singapore for skipping national service
According to his bio, writer Kevin Kwan was born in Singapore and left when he was 11, living in the USA since then. If convicted of draft-dodging, Kwan faces a three-year prison sentence and a fine of up to $7,300 (S$10,000).
Pakistan denies the allegation, saying it has acted effectively against all armed groups on its territory.
According to reports, the newly constituted Imran Khan's cabinet during its second meeting banned the discretionary use of state funds of the Prime Minister, federal ministers, members of the National assembly.
But the PTI leader has also vowed to have a "mutually beneficial relationship" with Washington.
Minutes after opposition chose to bring a joint candidate for presidential election, Information Minister Fawad Chaudhry said that the ruling Pakistan Tehreek-e-Insaf (PTI) has enough support to get their candidate elected to office, ARY News reported.
Khan is well known for his criticism of US military policy in Afghanistan, but he said after winning elections last week that he seeks better relations with the United States after a series of aid cuts and the suspension of USA military training. "I will never want Pakistan to be on the blacklist since it entails negative economic and other consequences", he said.
The Pakistani foreign minister said Pakistan's "strained ties" with the US have seen highs and lows and that the new government is determined to work to improve the relationship.