Along with Russia and the United States, France has for 20 years been trying to mediate a peace deal in the conflict, which saw Armenian separatists backed by Yerevan seize Karabakh from Azerbaijan in a war that claimed some 30,000 lives.
The conflict has simmered on, with frequent exchanges of gunfire and vows from Baku to retake the region by force.
Washington also hoped that Armenia and Azerbaijan “will agree to structure negotiations that will lead to a peace agreement,” she said.
“We call on both sides to redouble their efforts at the negotiation table and to focus on the benefits that peace will bring to people across the region,” Psaki said.
There has been an increase in violence in recent months along the Azerbaijan-Armenia border and at the Karabakh frontline, with both sides regularly accusing the other of tit-for-tat raids.
“Obviously inflammatory rhetoric and statements run counter the principle of reducing tensions,” Psaki added.