Confusion over the weekend's extraordinary events has left governments, both friendly and hostile to Moscow, groping for answers to what could happen next in a country that has the world's largest nuclear arsenal.
US Secretary of State Antony Blinken suggested the turmoil could take months to play out.
"We've seen more cracks emerge in the Russian facade," Blinken told NBC's "Meet the Press" programme on Sunday.
Russia's Deputy Foreign Minister Andrei Rudenko held talks in Beijing on "international" issues on Sunday. It was unclear if his visit to his country's strongest ally was precipitated by the Wagner mutiny.
"The Chinese side expressed support for the efforts of the leadership of the Russian Federation to stabilise the situation in the country in connection with the events of Jun 24 and confirmed its interest in strengthening the cohesion and further prosperity of Russia," the Russian foreign ministry said.
Beijing's response was characteristically measured. China's foreign ministry issued a statement vouching support for Russia's efforts to maintain national stability and referring to the recent tensions in the country as Russia's "internal affairs".
Ukrainian President Volodymyr Zelenskyy discussed the events in Russia in separate phone calls with US President Joe Biden and Canadian Prime Minister Justin Trudeau.
Biden and Trudeau both expressed their ongoing support of Ukraine as it pursues a counteroffensive to recover territory seized by Russia, according to official statements.
"The world must put pressure on Russia until international order is restored," Zelenskyy said on Twitter.
Putin said he was giving top priority to the conflict in Ukraine in excerpts from an interview aired by state television on Sunday that appeared to have been recorded before the mutiny.
State television said Putin would attend a meeting of Russia's Security Council this coming week, without elaborating, and Belarus' Belta news agency said Putin and Lukashenko spoke again on Sunday, after at least two calls on Saturday.
In a televised address during Saturday's drama, Putin said the rebellion put Russia's very existence under threat, vowing to punish those behind the revolt and drawing parallels with the chaos of 1917 that had led to the Bolshevik revolution.
"The myth of the unity of Putin's Russia is over ... It's the inevitable outcome when you support and finance a legion of mercenaries," Italy's Foreign Minister Antonio Tajani was quoted as saying by Italian newspaper Il Messaggero.
PRIGOZHIN'S WHEREABOUTS UNKNOWN
Under the deal, brokered late on Saturday, Kremlin spokesman Dmitry Peskov said a criminal case opened against Prigozhin for armed mutiny would be dropped, Prigozhin would move to Belarus, and Wagner fighters who rallied to his cause would face no action, in recognition of their previous service to Russia.
Prigozhin, 62, was seen leaving the district military headquarters in Rostov late on Saturday in a sport utility vehicle. His whereabouts since were not known.
A former Putin ally and ex-convict whose forces have fought the bloodiest battles of the 16-month war in Ukraine, Prigozhin said his decision to advance on Moscow was intended to remove corrupt and incompetent Russian commanders he blames for botching the war.
This month, Prigozhin defied orders to place his troops under Defence Ministry command. He launched the rebellion on Friday after alleging the military had killed some of his men in an air strike. The Defence Ministry denied this.
Wagner, whose men in Ukraine include thousands of ex-prisoners recruited from Russian jails, has grown into a sprawling international business with mining interests and fighters in Africa and the Middle East.
Serhiy Nayev, commander of Ukraine's Joint Forces responded to speculative reports that Wagner fighters could be moved to Belarus to attack Ukraine from the north.
"If this happens and the enemy tries to cross the state border, it will be nothing but a suicide for them,” Nayev said in a post on the military's Telegram account.