Moscow Mayor Sergey Sobyanin said "anti-terrorist measures" are being taken in the city.
Armored vehicles were sent into Moscow amid heightened security.
Rostov region Governor Vasily Golubev urged residents not to leave their homes.
Generals accused Prigozhin of an ''attempted coup'' with Russia's top commander in Ukraine, Sergey Surovikin, urging Wagner fighters to obey Russian President Vladimir Putin.
The Russian Federal Security Service said Prigozhin's actions were a ''stab in the back'' and accused him of inciting an ''armed rebellion.''
It urged Wagner fighters not to carry out his ''criminal and treacherous'' orders and to detain their leader.
Prigozhin defied Russian forces and threatened to destroy anyone who stands in the group’s way.
He said his forces in Ukraine have crossed into the Russian city of Rostov in a voice message shared on the Telegram social media platform.
Prigozhin also said his forces shot down a Russian military helicopter.
Kremlin spokesman Dmitry Peskov said Putin has been fully briefed on the situation with Prigozhin and that all necessary measures are being taken.
Meanwhile, Russia's National Anti-Terrorism Committee opened a criminal case against Prigozhin on charges of incitement to armed rebellion and demanded he "stop the illegal actions."
Earlier, Progozhin shared a voice message on Telegram that claimed Russian forces had attacked his paramilitary group.
After a reported rocket strike on Wagner, Prigozhin accused the Russian Defense Ministry and personally swore to "punish" the perpetrators and Defense Minister Sergey Shoygu.
"There's 25,000 of us and we're coming to figure out why there's such chaos in the country," said Prigozhin. “These 25,000 are waiting as a tactical reserve, and the strategic reserve is the whole army and the whole country. Anyone who wants come and join! We need to end this mess.''
He then claimed that Shoygu came to the Russian city of Rostov-on-Don to "carry out an operation to destroy Wagner," adding that he used artillerymen and helicopter pilots "in the dark."
Prigozhin claimed Thursday that Russian military chiefs are deceiving Putin.
He highlighted a discrepancy between his information and official data, claiming “shameless lies are being brought to the president's desk."
He added that he expects a new wave of military mobilization in Russia and said: "People have to be prepared" to replace soldiers who have died in battle.
Prigozhin has, in recent months, repeatedly accused the Russian Defense Ministry and Shoygu of not supplying sufficient arms to the paramilitary group, members of whom are fighting with Ukrainian forces in year two of the Ukraine war.
Earlier, the Wagner leader claimed Ukraine's armed forces were 25 kilometers (15.5 miles) from Russian positions in the Zaporizhzhia region. At the same time, the Russian Defense Ministry reported that all of Ukraine's attacks were repulsed.
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