Russian authorities said Tuesday they have closed a criminal investigation into the armed rebellion led by mercenary chief Yevgeny Prigozhin, with no charges against him or any of the other participants.

The Federal Security Service, or FSB, said its investigation found that those involved in the mutiny “ceased activities directed at committing the crime,” so the case would not be pursued.

The announcement was the latest twist in a series of stunning events in recent days that have brought the gravest threat so far to President Putin’s grip on power amid the 16-month-old war in Ukraine.

Over the weekend, the Kremlin pledged not to prosecute Mr. Prigozhin and his fighters after he stopped the revolt on Saturday, even though Putin had branded them as traitors.

The charge of mounting an armed mutiny carries a punishment of up to 20 years in prison. Mr. Prigozhin escaping prosecution poses a stark contrast to how the Kremlin has treated those staging anti-government protests in Russia.

Many opposition figures in Russia have received long prison terms and are serving time in penal colonies notorious for harsh conditions.

The whereabouts of Mr. Prigozhin were unknown as of Tuesday. The Kremlin has said he would be exiled to neighboring Belarus, but neither he nor the Belarusian authorities have confirmed that.

An independent Belarusian military monitoring project, Belaruski Hajun, said a business jet that Mr. Prigozhin reportedly uses landed near Minsk on Tuesday morning.

The media team for Mr. Prigozhin, the 62-year-old head of the Wagner private military contractor, did not immediately respond to a request for comment.

Belarus’ authoritarian president, Alexander Lukashenko, a close Putin ally who brokered a deal with Mr. Prigozhin to stop the uprising, didn’t immediately address Mr. Prigozhin’s fate in a speech Tuesday.

Mr. Lukashenko, who has ruled Belarus with an iron hand for 29 years, relentlessly stifling dissent and relying on Russian subsidies and political support, portrayed the uprising as the latest development in a clash between Mr. Prigozhin and Russia’s defense minister, Sergei Shoigu. Their long-simmering personal feud has at times boiled over, and Mr. Prigozhin has said the revolt aimed to unseat Mr. Shoigu, not Putin.

Mr. Lukashenko framed the insurrection by Wagner as a significant threat, saying he placed Belarus’ armed forces on a combat footing as the mutiny unfolded.

Like Mr. Putin, he couched the Ukraine war in terms of an existential threat to Russia, saying: “If Russia collapses, we all will perish under the debris.”

In a nationally televised address Monday night, Mr. Putin once again blasted organizers of the rebellion as traitors who played into the hands of Ukraine’s government and its allies. Although he was critical of Prigozhin, Mr. Putin praised the work of Wagner commanders.

That was “likely in an effort to retain them” in the Russian effort in Ukraine, because Moscow needs “trained and effective manpower” as it faces the early stages of a Ukrainian counteroffensive, according to a Washington-based think tank.

The Institute for the Study of War also noted that the break between Messrs. Putin and Prigozhin is likely beyond repair and that providing the Wagner chief and his loyalists with Belarus as an apparent safe haven could be a trap.

Mr. Prigozhin’s short-lived insurrection over the weekend has rattled Russia’s leadership.

Mr. Putin sought to project stability in his speech, criticizing the uprising’s “organizers,” without naming Mr. Prigozhin. He also praised Russian unity in the face of the crisis, as well as rank-and-file Wagner fighters for not letting the situation descend into “major bloodshed.”