"It is clear that we believe that any unilateral action by them (Turkey) would be unacceptable," Esper told reporters traveling with him to Japan.
"What we will do is prevent unilateral incursions that would once again disturb these mutual interests that the United States shares with both Turkey and the SDF regarding northern Syria."
He said he hoped to reach an agreement with Ankara on the "safe area."
The Associated Press quoted Esper as saying he believed they had "made progress on some key issues."
Esper said Turkey was a long-term US ally, noting that the SDF issue was not new and markedly different from an ally buying a Russian-built air defense system that could threaten a US aircraft.
Esper also said the United States would not abandon its allies in the SDF.
Turkey is threatening to launch attacks on the northern and eastern regions of Syria to achieve a number of objectives, including the eradication of the Kurds and their displacement from their areas and changing the demography of the region as is happening now in the occupied city of Afrin, as well as controlling the Syrian oil and gas sources, as well as the elimination of the democratic experience that develops in the region through the participation of all peoples in the region in their management.