The fighters of the Wagner private army run by Yevgeny Prigozhin, a former ally of Russian President Vladimir Putin, were already most of the way to the capital, having captured the city of Rostov and setting off on an 1,100 km (680 mile) race to Moscow, Reuters reported on Saturday.
In an audio message, Prigozhin said the fighters would return to base because of the risk of blood being spilled.
A deal to halt further movement of Wagner fighters across Russia in return for guarantees of safety for the rebels was brokered by Belarusian President Alexander Lukashenko, his office said.
Earlier, Prigozhin said his men were on a march to remove Russian commanders he blames for botching the war in Ukraine.
In a televised address from the Kremlin, Putin had said Russia's very existence was under threat because of the mutiny.
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