The U.S., Russian and French mediators urged Azerbaijan on Saturday to accept their long-standing proposal to set up a mechanism for international investigations of ceasefire violations in the Nagorno-Karabakh conflict zone.

“Armenia has agreed to discuss the details of the mechanism, and we urged Azerbaijan to do the same,” the three co-chairs of the OSCE Minsk Group said one day after hosting fresh talks in New York between the foreign ministers of the two states.

The talks were overshadowed by recent days’ fresh escalation of fighting along “the line of contact” around Karabakh and the Armenian-Azerbaijani border, which has left about a dozen soldiers and civilians dead.

“The Co-Chairs condemned in strong terms the use of artillery that caused additional casualties in the last twenty-four hours,” read a joint statement issued by them. “We extend our deepest condolences to the families of the deceased. An escalation of violence is not in the interest of Azerbaijanis or Armenians, or a negotiated settlement.”

The mediators said that they discussed with Foreign Ministers Edward Nalbandian and Elmar Mammadyarov the “immediate need to reduce tensions” on the frontlines. They believe that an “OSCE mechanism to investigate ceasefire violations” would help to defuse tensions.

Armenia and Karabakh’s ethnic Armenian leadership have repeatedly said that they support the idea. Nalbandian reaffirmed this stance during the talks with Mammadyarov.

By contrast, Azerbaijan has objected to the proposed investigations until now. Its leaders have said that such an arrangement would be meaningless in the absence of an Armenian-Azerbaijani peace deal.

Significantly, the mediating troika also announced on Saturday that the two ministers “agreed to continue preparations with the Co-Chairs” for a meeting of the Armenian and Azerbaijani presidents. The summit is “expected to be held before the end of this year,” it said.