The YPG, which forms the backbone of the Syrian Democratic Forces (SDF), the Kurdish-Arab alliance that has received extensive American backing, vowed Tuesday it would withdraw.
Cavusoglu told Agence France-Presse in an interview that the move was a key part of rebuilding ties with Washington damaged by a string of rows including Syria and also issues such as American citizens detained in Turkey.
"The US couldn't keep its promises in the past. But I think they also understood that it is a very critical issue, and this is why we agreed to work," Cavusoglu told AFP in his home southern region of Antalya where he is campaigning for Turkey's June 24 elections.
"The implementation of this roadmap will help us actually to rebuild the mutual trust between two allies," he added.
But he warned that the plan now had to be implemented on the ground. "If not, there will be a lack of trust," he said.
Tensions between Washington and Ankara have so far scotched expectations of a strong alliance emerging between President Donald Trump and his Turkish counterpart Recep Tayyip Erdogan.
Cavusoglu expressed scepticism over the vow to withdraw by the YPG, who Turkey accuses of being the Syrian branch of the outlawed Kurdistan Workers' Party (PKK).
"I'm not sure they are leaving," said Cavusoglu.
"I have seen that in the press, but in the past also the US had told us that they had left and they didn't. For me, what the YPG is saying is no kind of truth. We have to make sure that they leave."
He said the aim of the roadmap is to ensure that the YPG leaves Manbij and then have the US and Turkey work together to establish a local security structure and "decide together who is going to govern Manbij.
"This is the aim, so now it is time to implement it," he said.
He said the assurance of stability in the area would encourage the return home of Syrian refugees, some 3.5 million of whom live in Turkey.
Turkish forces earlier this year ousted the YPG from the Afrin region of northern Syria in a military operation.
But Cavusoglu indicated that he wanted similar agreements with the US to prise the YPG from towns it had seized from Islamic State (IS) jihadists with American backing close to the Turkey border.
Turkey has repeatedly accused the YPG of unbalancing the pre-war ethnic balance of towns like the former IS de-facto capital of Raqa which were predominantly Arab.
"Eventually they should also leave from other areas... because Raqa for instance is a 90 percent Arab city," said Cavusoglu.
Ankara has long opposed the YPG controlling a continuous stretch of territory on its border up to Iraq, fearing the creation of an autonomous region or even independent entity that could embolden Turkey's own Kurds.
"A terrorist should not rule any areas. We are not against Kurds but against PKK and YPG," said Cavusoglu.
Ahead of the elections, top officials including Erdogan have increasingly evoked the possibility of a Turkish operation against the bases of the PKK's military leadership in the Qandil mountains of northern Iraq.
Pressed on the possibility of such an operation, Cavusoglu said: "We will eliminate (them) wherever they are. The threat is there and we have to eliminate it."
![Russian Deputy Defence Minister, Timur Ivanov [PhotoNews Pakistan]](data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D'http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg'%20width%3D'300'%20height%3D'172'%20data-ring-placeholder%3D'1'%3E%3C%2Fsvg%3E "Russian Deputy Defence Minister, Timur Ivanov [PhotoNews Pakistan]")