NAIROBI, Kenya (AP) — The Tigray forces battling Ethiopian troops say they’re willing to abide by an immediate cessation of hostilities and participate in a peace process led by the African Union, a significant shift to which the government has not yet responded.

The conflict in northern Ethiopia’s Tigray region has killed an estimated tens of thousands of people and left millions without basic services for well over a year after fighting erupted in late 2020.

The Tigray authorities’ statement Sunday night came after new pressure by the United States and others following the renewal of fighting last month that shattered months of relative calm.

The Tigray authorities had criticized AU mediation efforts under special envoy Olesegun Obasanjo, and their new statement makes clear they expect “mutually acceptable mediators” along with international observers and experts to guide the process.

The Ethiopian government has said it was ready for talks anywhere at any time and without preconditions. Tigray authorities had demanded the resumption of basic services and the removal of hostile forces from neighboring Eritrea, among other things.

The U.S., AU and United Nations welcomed the Tigray authorities’ new statement, and the U.S. called on Eritrea and unnamed “others” to stop fueling the conflict.