The future of Wagner and Prigozhin has been unclear since he led a short mutiny against the Russian defense establishment in late June.
Authorities instituted a temporary restriction on the presence of any aircraft in the airspace above Moscow after the attack.
Russia used Iranian-made Shahed drones to attack Kyiv for the sixth time this month, but all were shot down, said Serhiy Popko, head of the Kyiv military administration.
"All ships proceeding to Ukrainian ports in Black Sea waters will be considered as potential carriers of military cargo," the Russian Defense Ministry stated.
The advances brought the total territory recaptured so far during the counteroffensive to more than 210 sq km, she said in updates on the Telegram messaging app.
Ukraine said its troops had regained more ground on the eastern and southern fronts, while an official said fighting had surged around the city of Bakhmut.
According to preliminary information, there were no casualties or damage.
Experts argue that the stark deviation from Putin's usual behavior and security protocols points to the involvement of a body double.
The group called on Ukraine's government to follow through with a commitment made earlier this month not to employ such weapons.
An ally of Russian President Vladimir Putin said that the Wagner mercenary group only advanced so quickly because all of Russia's forces were focused on defending Moscow.