In a video on social media, Prigozhin appeared inside a plane flying in darkness, wearing a helmet and a pilot mask.
"We are landing, we bombed Bakhmut," the businessman and Kremlin ally said.
"If you have the will, we will meet in the skies. If you win, you will take Artemovsk (the Russian name for Bakhmut), if not, we will go until the Dnipro (River)," Prigozhin said.
The same day, Ukraine's parliament adopted a resolution denouncing Wagner, whose mercenaries are fighting alongside Russian troops, as a terrorist organisation.
"We are preparing to destroy Wagner as a component of international terrorism," the head of the Ukrainian presidential administration, Andriy Yermak, said.
He said the recognition was a "step towards bringing them (Wagner) to justice."
Wagner mercenaries are taking part in Moscow's offensive on Bakhmut, which Russia has been trying to capture for months, with heavy losses on both sides.
Zelensky on Saturday vowed to fight for Bakhmut "as long as we can."