Story highlights Icy comments come in wake of fresh US sanctions over Crimea

Russia hopes for "constructive dialogue" under Trump presidency

(CNN) The frosty relationship between the United States and Russia has become even more icy after Moscow said communications between the countries were at the bare minimum.

"Nearly all levels of our dialogue (with the US) has been frozen," Kremlin spokesman Dmitry Peskov said in an interview Wednesday with Russian state-run news agency RIA Novosti.

"We do not talk to each other. Or we do it to a minimum," he said.

But US State Department spokesman John Kirby had a different take, saying in a statement: "Diplomatic engagement with Russia continues across a wide range of issues."

Indeed, US Secretary of State John Kerry spoke on the phone this week with Russian Foreign Minister Sergey Lavrov about the situation in Syria, Kirby said.