It comes as local residents of Kherson report hearing the sounds of gun battles and tank fire in the city and its environs.
On Monday, Natalia Humeniuk, a spokeswoman for Ukraine’s southern command, confirmed that Kyiv had launched its counteroffensive in the Kherson region.
Reports soon emerged of a major breakthrough by Ukrainian forces, as Russian troops were quickly routed.
Oleksiy Arestovych, a senior adviser to President Zelensky, claimed that Ukraine’s army had broken though Russian defences in several sectors of the frontline near the city of Kherson.
Now, local residents claim that Russian soldiers are surrendering en masse and fleeing from the battlefield.
Social media Katerina posted on her Twitter account: “I talked with a friend from Kherson.
“He wrote that the Russian military are surrendering en masse.
“The rest are fleeing from Kherson and the region, everyone wants to live.
“The mood is decadent, no one wants to die for Putin.”
A Russian military blogger, going by the name Moscow Calling, said gun battles and tank rounds could be heard in Kherson and its environs.
He wrote: “They report about a small-arms battle, shots from tanks and infantry fighting vehicles.
“This is not just somewhere, but in Kherson itself.”
His post was accompanied by a video, purportedly shot by a Kherson resident, in which sounds of a raging battle can be distinctly heard.
Despite its early successes, Kyiv is keen to dampen down expectations of a swift victory in its counterattack.
Mr Arestovych said the counteroffensive was a “planned slow operation to grind the enemy”.
Moscow Calling said: “To believe the reports about the repulse of the counter-offensive is to believe the stories of the night of February 24 – ‘Kyiv is taken by anti-fascists, the air defence of Ukraine is destroyed, Kharkov is ours.’
“After all, the same people write, or rather, the same war rats.
“The real situation will be clear in weeks, if not months.”
“But somehow I don’t care anymore, the Russian Federation lost the war about five months ago.”