Syria's government, meanwhile, described the agreement as a serious escalation that violates its sovereignty.
Wednesday's announcement did not address these two points of disagreement, but it did appear to head off a new influx of Turkish troops into northeastern Syria.
The US, however, supports the militia as the main fighting force against the Islamic State group.
The State Department later said that while additional details need to be fleshed out "we are encouraged by the initial steps that came out of these talks".
But Cavusoglu added that his government will not let the implementation of this agreement stall like a previous deal with Washington reached past year.
"We will not allow these efforts (on the safe zone) to turn into the Manbij roadmap", Cavusoglu said. Turkey urges Washington to collect all the heavy weapons it delivered to the YPG during its fight against the IS. It offered few other details.
The U.S. has supported the Syrian Kurdish fighters as its main fighting force against the Islamic State (IS) group in Syria and sought to find a midway between the concerns of its North Atlantic Treaty Organisation ally and its main partner on the ground in Syria.
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The U.S. has seen this and stepped up to "make this together", Cavusoglu added.
In response to Erdogan's statement, US Defence Secretary Mark Esper said that the US would "prevent any unacceptable offensive" by Turkey against the YPG.
"Humanitarian actors are increasingly concerned by statements suggesting possible military intervention, which would have severe humanitarian consequences in an area which has already witnessed years of military activity, displacement, droughts and floods", he added.
Kurdish troops there. About 1,000 USA troops are also stationed in Syria and could be placed in danger by a Turkish attack. If the army keeps pushing into the northwest, Syrian forces could get in contact with Turkish troops that man 12 observation posts along the border of Idlib.
"Our plans on the Syrian safe zone and the deployment of our troops in the field have been completed", he said, but noted that Ankara wants to realize the safe zone with the U.S. "Turkish project" and align with the Syrian government instead.
Damascus has had no presence along the Turkish border since 2012, when Syrian rebels and Syrian Kurdish groups took control of different parts of the region.
It wants the region to be cleared of Syrian Kurdish forces and has threatened on numerous occasions to launch a new operation in Syria against Syrian Kurdish forces if a safe zone is not established.
Syrian state-run media say government forces have captured a northwestern village and are getting closer to the town of Kfar Zeita, which has been held by insurgents since 2012.