Svetlana Tikhanovskaya also expressed concern that Wagner would be used to further oppress the people of Belarus.
The New York Times reported that American officials also said there were signs that other Russian generals also may have supported Prigozhin.
Iran said it supports the rule of law in the Russian Federation and considers the latest developments there an internal Russian matter.
Belarus allowed Russia to use it as one of the launchpads for its full-scale invasion of Ukraine last year. It has held frequent exercises with Russia and let Russian forces use its bases.
The deployment of nuclear weapons in Belarus is Moscow's first move of such warheads outside Russia since the fall of the Soviet Union.
Zakharova insisted that Russia was intent on maintaining the principle that nuclear war was inadmissible.
The deployment is Moscow's first move of such warheads outside Russia since the fall of the Soviet Union.
Putin announced in March he had agreed to deploy such weapons in Belarus, pointing to US deployment of tactical nuclear weapons in a host of European countries over many decades.
The Security Council is the only UN body that can make legally binding decisions such as imposing sanctions and authorizing use of force.