The Saturday phone call was held at the initiative of the Iranian side.
"The Iranian side expressed support for the actions of the Russian leadership to ensure constitutional order," the Russian Foreign Ministry said in a Saturday statement.
The foreign ministers also discussed Russian-Iranian agenda and regional and international topics.
On Friday, the Russian Federal Security Service (FSB) opened a criminal case for inciting armed mutiny over statements made on behalf of Yevgeny Prigozhin, the head of the Wagner Group private military company (PMC). The FSB said that there was a threat of escalation on Russian territory. The Russian Defense Ministry said that social media reports of alleged Russian military strikes on PMC Wagner camps were not true.
Russian President Vladimir Putin delivered a televised address to the nation on Saturday in which he described the actions of the Wagner Group as an armed mutiny and treason, and promised harsh measures against the insurgents.
Later in the day, the Belarusian presidential office said that Prigozhin accepted the proposal of Belarusian President Alexander Lukashenko to stop the movement of Wagner troops in Russia and take further steps to de-escalate the situation. Prigozhin later confirmed the information, saying that Wagner troops were returning back to their field camps.
Nicaraguan President Daniel Ortega has expressed his solidarity and support in a letter to Russian President Vladimir Putin amid the Saturday events, saying that the Russian government and people are facing a moment of challenge to the character, identity, wisdom and strength of Russia.
Israeli Prime Minister Benjamin Netanyahu held a special meeting on Saturday night with the heads of key governmental departments, discussing the situation in Russia. Netanyahu said that the events concerning Wagner Group were Russia’s internal affair but Israel was going to continue monitoring the developments.
Kremlin spokesman Dmitry Peskov told reporters on Saturday evening that the criminal case against Prigozhin would be terminated and he would leave for Belarus under guarantees given by Putin. The spokesman added that members of the Wagner PMC who were involved in the Saturday events would not be prosecuted given their distinguished service during Russia's special military operation in Ukraine.