The announcement comes a day before U.S. Secretary of State Rex Tillerson is set to land in Turkey for his first face-to-face meetings with President Recep Tayyip Erdogan and other top leaders.
On Wednesday, Turkish Prime Minister Binali Yildirim announced the operation had ended after its troops and allied rebels secured territory along the border between Turkey and Syria.
It is particularly frustrated by the use of YPG fighters in a planned USA -led offensive to retake Islamic State's Syrian stronghold of Raqqa, an operation in which Ankara has long said it wants to play a role. "Let me be very frank, it's not easy, they are hard choices that have to be made".
Turkey, sheltering more than 2 million Syrians, has long called for such safe areas but the idea has gained little traction among Western allies who question how such zones can be carved out without a significant foreign military presence.
Tillerson and Yildirim "discussed working to enhance our critical security and economic ties in the region", a State Department official said after the meeting.
However, this was met with disagreement from Cavusoglu, who complained about USA support for the Syrian Kurdish YPG militia, considered a terrorist group by Ankara.
Ankara, however, views the YPG as an extremist group, part of Kurdish separatists the Kurdistan Workers' Party (PKK).
"The fact [Trump] is not putting pressure for domestic reforms, liberal reforms or attention to human rights [in Turkey] certainly removes one obstacle and certainly makes Trump seem like somebody that Erdogan could more easily work with", Leslie Vinjamuri, an associate fellow at Chatham House's USA and the Americas tells Newsweek.
There are multiple sources of friction: Washington has so far refused to extradite Fethullah Gulen, the Muslim cleric Ankara accuses of engineering the failed July 15 coup.
The PKK has led a three-decade long insurgency in southeast Turkey and is considered a "terrorist group" by the US.
Still, Trump, who spoke in glowing terms about Erdogan during the US presidential campaign, has shown no sign of deviating from Obama-era policies that had so angered Turkey, including a reliance on the Syrian Kurdish force, known as the YPG.
The US sees the YPG as a main ally in fighting Daesh, but Turkey considers it as a branch of the PKK terror group.
The decision has "negatively affected the Turkish people's sentiments towards the United States", said Cavusoglu.
"We want to see some concrete evidence on the details of this issue", to confirm the USA account of the July 21 call to Adil Oksuz, he said.
"Operation Euphrates Shield has been successful and is finished". At a minimum, he said Turkey wants the U.S.to arrest Gulen while weighing the extradition. In the months since Trump took office, the United States and Turkey have managed to avoid any open confrontation over their differences, with Turkish officials showing optimism that the relationship could only improve.