Members of the mercenary Wagner Group have begun moving north "almost certainly aiming to get to Moscow," in what amounts to the "most significant challenge to the Russian state in recent times," the U.K. Ministry of Defense said on Saturday.

"Over the coming hours, the loyalty of Russia's security forces, and especially the Russian National Guard, will be key to how the crisis plays out," the ministry said on Twitter.

Russian President Vladimir Putin said moves taken by Wagner Group leader Yevgeny Prigozhin, a longtime ally, to bring his troops into a key Russian city amounted to a "stab in the back."

Putin didn't mention Prigozhin by name, but said that "necessary orders have been given" to defend Russia in a recorded address aired on Russian television on Saturday.

"Actions that divide our unity are in essence defeatism before one's own people," he said. "This is a stab in the back of our country and our people."

-ABC News' KJ Edelman

Russian President Vladimir Putin has been briefed by the country's security agencies about what was referred to as an "attempted armed rebellion," according to Russia's state-run media.

The late-night statement from Putin's spokesman suggested that the Kremlin considered Wagner Group's move into Rostov-on-Don, a key Russian city close to the border with Ukraine, to be a "rebellion."

Wagner's founder Yevgeny Prigozhin in an audio message on Friday claimed his forces would now punish Russia's defense minister and chief of general staff, telling other units to stand down and not offer resistance.

"Special services, law enforcement agencies, namely the Ministry of Defense, the FSB, the Ministry of Internal Affairs, Rosgvardiya, in round-the-clock mode, constantly report to the president on the measures taken in the context of the implementation of the instructions previously given to him," Kremlin spokesperson Dmitry Peskov said on Saturday.

-ABC News' Tanya Stukalova and Patrick Reevell

The Wagner Group is a private military organization run by Yevgeny Prigozhin, a longtime ally of Russian leader Vladimir Putin, with tens of thousands of fighters, according to U.S. officials.

Earlier this year, the U.S. labeled the group a "significant transnational criminal organization" and levied new sanctions, while human rights observers this week said they suspected Wagner fighters were linked to the mass killing of people in Mali last year.

Government reports, statements from U.S. officials and insights from experts, as well as other sources, shed light on the Wagner group's history and goals, its alleged wrongdoings and its importance to Russia -- in Ukraine and elsewhere in the world.

-ABC News’ Nathan Luna, Leah Vredenbregt and Ivan Pereira

President Volodymyr Zelenskyy again called on Tuesday for NATO to invite Ukraine to become a member, offering a strongly worded statement as the coalition leaders gathered for a summit in Lithuania.

Ukraine "deserves respect," Zelenskyy said in a statement posted on Twitter.

"It's unprecedented and absurd when time frame is not set neither for the invitation nor for Ukraine's membership," he said. "While at the same time vague wording about 'conditions' is added even for inviting Ukraine. It seems there is no readiness neither to invite Ukraine to NATO nor to make it a member of the Alliance."

Keeping Ukraine out of NATO amounts to a "motivation" for Russia to "continue its terror," he said.

"Uncertainty is weakness," he added.

Russia rebutted the statement a short while later.

"This is potentially very dangerous for European security. Indeed, it is fraught with great dangers, and those who will make this decision should be aware of that," Dmitry Peskov, a Kremlin spokesperson, said when asked to comment on Ukraine's possible fast-track admission to the coalition.