"With the aim of preventing possible terrorist acts on the territory of the city of Moscow and the Moscow region, an anti-terror operation regime has been introduced," the country's national anti-terrorist committee said in a statement quoted by Russian agencies.

Russia also declared an anti-terrorist operation in the southern Voronezh region, where some reports said Wagner mercenaries were also headed.

Moscow Mayor Sergei Sobyanin said the measure was "aimed at strengthening security."

He also said there was "additional control" on roads and that the capital's mass events may be limited.

The announcement came as Wagner chief Yevgeny Prigozhin said he had crossed into Russia and seized control of a key military headquarters, vowing to topple Moscow's military leadership and saying he and his 25,000 fighters were "ready to die".

Yevgeny Prigozhin, 62, said his forces, who have spearheaded much of Russia's offensive in Ukraine, had entered the southern Russian city of Rostov-on-Don and controlled its military sites.

"We are inside the (army) headquarters, it is 7:30 am (0430 GMT)," Prigozhin said in a video on Telegram.

"Military sites in Rostov, including an aerodrome, are under control," he added.

Russia's military headquarters in Rostov-on-Don are a key logistical base for its offensive in Ukraine.

Prigozhin said planes taking part in the Ukraine offensive "are leaving as normal" from the airfield, and called on Russians not to believe what they were being told on state television.

"A huge amount of territory is lost. Soldiers have been killed three, four times more than it says in documents shown to the top (leadership)."

In the video from Rostov, Prigozhin also claimed Russia's chief of General Staff Valery Gerasimov "ran away from here when he found out that we are approaching the building."

He has vowed to topple Gerasimov and Defence Minister Sergei Shoigu.

A Wagner-linked Telegram channel on Saturday published another video of what it said was Prigozhin talking with two army officials in the Rostov headquarters.

​He told the military officials that his mercenaries will "not interfere with them commanding troops" and said their orders in Ukraine were leading to huge losses.

Videos and pictures posted online, including by the TASS state-run news agency, showed armed men surrounding administrative buildings in Rostov and tanks deployed in the city centre. It was not clear who the armed men were.

President Vladimir Putin was due to make a televised address on Saturday, Kremlin spokesman Dmitry Peskov told Russian news agencies.

Authorities in Rostov have urged residents to stay at home.

Russia opened a criminal case against Prigozhin, accusing him of trying to start an "armed rebellion."

The Russian army said it would "guarantee the safety" of Wagner mercenaries who stop rebelling against Moscow's military leadership.

"We are appealing to the fighters of assault squads of PMC Wagner. You were deceived into (Wagner chief's Yevgeny) Prigozhin's criminal venture and participation in an armed rebellion," the army said in a statement. It called on the fighters to ask for help to return to "places of permanent deployment."

"We ask you to show reason and get in touch with representatives of Russia's defence ministry or law enforcement. We guarantee safety for all."

On Friday, the National Anti-Terrorism Committee, which is part of the Federal Security Services, or FSB, charged Prigozhin with calling for an armed rebellion, punishable by up to 20 years in prison.

The FSB urged Wagner’s contract soldiers to arrest Prigozhin and refuse to follow his “criminal and treacherous orders.” It called his statements a “stab in the back to Russian troops” and said they amounted to fomenting armed conflict.

Putin was informed about the situation and “all the necessary measures were being taken,” Kremlin spokesperson Dmitry Peskov said. On Saturday morning he added that Putin would address the nation “shortly.”