Russian mercenary boss Yevgeny Prigozhin said on Saturday (local time) his Wagner fighters had crossed the border into Russia from Ukraine and were prepared to go "all the way" against Moscow's military, hours after the Kremlin accused him of armed mutiny.

As a long-running standoff between Prigozhin and the military top brass appeared to come to a head, Russia's FSB security service opened a criminal case against him, TASS news agency said. It called on the Wagner private military company forces to ignore his orders and arrest him.

Wagner fighters had entered the southern Russian city of Rostov, Prigozhin said in an audio recording posted on Telegram. He said he and his men would destroy anyone who stood in their way.

Prigozhin earlier said, without providing evidence, that Russia's military leadership had killed a huge number of his troops in an air strike and vowed to punish them.

He said his actions were not a military coup. But in a frenzied series of audio messages, in which the sound of his voice sometimes varied and could not be independently verified, he appeared to suggest that his 25,000-strong militia was en route to oust the leadership of the defence ministry in Moscow.

Security was stepped up on Friday night at government buildings, transport facilities and other key locations in Moscow, TASS reported, citing a source at a security service.

Russian President Vladimir Putin was getting around-the-clock updates, TASS said, while the White House said it was monitoring the situation and would consult with allies.

Kyiv, meanwhile, said the major thrust in its counteroffensive against Moscow's invasion had yet to be launched. "The main blow is still to come," Deputy Defence Minister Hanna Maliar told Ukrainian television.

A top Ukrainian general reported "tangible successes" in advances in the south - one of two main theatres of operations, along with eastern Ukraine.

'OBEY PRESIDENT,' GENERAL SAYS

The deputy commander of Russia's Ukraine campaign, General Sergei Surovikin, told Wagner fighters to obey Putin, accept Moscow's commanders and return to their bases. He said political deterioration would play into the hands of Russia's enemies.

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"I urge you to stop," Surovikin said in a video posted on Telegram, his right hand resting on a rifle.

The standoff, many of the details of which remained unclear, looked like the biggest domestic crisis Putin has faced since he sent thousands of troops into Ukraine in February last year.

Prigozhin, a one-time Putin ally, in recent months has carried out an increasingly bitter feud with Moscow. Earlier on Friday, he appeared to cross a new line, saying the Kremlin's rationale for invading Ukraine, which it calls a "special military operation," was based on lies by the army's top brass.

Wagner led Russia's capture of the Ukrainian city of Bakhmut last month, Russia's biggest victory in 10 months, and Prigozhin has used its battlefield success to criticise the leadership of the defense ministry with seeming impunity - until now.

For months, he has openly accused Defence Minister Sergei Shoigu and Russia's top general, Valery Gerasimov, of incompetence.

Army Lieutenant-General Vladimir Alekseyev issued a video appeal in which he asked Prigozhin to reconsider his actions. "Only the president has the right to appoint the top leadership of the armed forces, and you are trying to encroach on his authority," he said.

UKRAINE SAYS MAJOR THRUST AHEAD

On the ground in Ukraine, at least three people were killed in Russian attacks on Friday, including two who died after a trolleybus company came under fire in the city of Kherson, regional officials said.

Addressing the pace of the Ukrainian advances, several senior officials on Friday sent the clearest signal so far that the main part of the counteroffensive has not yet begun.

"I want to say that our main force has not been engaged in fighting yet, and we are now searching, probing for weak places in the enemy defences. Everything is still ahead," the Guardian quoted Oleksandr Syrskyi, the commander of Ukraine's ground forces, as saying in an interview with the British newspaper.

General Oleksandr Tarnavskyi, commander of Ukraine's "Tavria," or southern front, wrote on Telegram: "There have been tangible successes of the Defence Forces and in advances in the Tavria sector."

Tarnavskyi said Russian forces had lost hundreds of men and 51 military vehicles in the past 24 hours, including three tanks and 14 armoured personnel carriers.

Although the advances Ukraine has reported this month are its first substantial gains on the battlefield for seven months, Ukrainian forces have yet to push to the main defensive lines that Russia has had months to prepare.