In footage shared on social media, the lone man - who has been identified as Tymofiy Shadura - smokes a cigarette in a clearing in a forest while Russian guns are pointed at him.
In his last moments he defiantly says "slava Ukraini" - the Ukrainian war motto meaning ‘Glory to Ukraine” - before being shot to death in bursts of gunfire.
Mr Shadura was a soldier who served in the 30th Brigade of the Ukrainian armed forces. He had been missing since February 3, according to reports.
"We will find the murderers," Ukrainian President Zelensky said late on Monday.
In his video address, Mr Zelensky said "the occupiers" killed "a warrior who bravely said to their faces: ‘Glory to Ukraine!’"
"I want us all to respond to his words together, in unity: ‘Glory to the Hero! Glory to the Heroes! Glory to Ukraine!’"
Mr Zelensky was referring to a battle cry in Ukraine’s military that has become popular among millions of Ukrainians.
A woman, who claimed to be Mr Shadura’s sister, told the BBC: “My brother would certainly be capable of standing up to the Russians like that.
“He never hid the truth in his life and certainly wouldn’t do so in front of the enemy.”
Andriy Yermak, Mr Zelensky’s chief of staff, said: "There will be retribution for every such war crime. No one can hide from her. We will find everyone."
Dmytro Kuleba, the Ukrainian foreign minister, called on the International Criminal Court to launch an immediate investigation into the footage.
It came as Yevgeny Prigozhin, the Russian mercenary boss, "sent a truckload of champagne" made in Bakhmut to Ukrainian women to mark International Women’s Day in a social media stunt.
The Kremlin-linked tycoon shared footage of him helping load the sparkling wine onto a lorry as fighters from his Wagner Group appeared on the cusp of victory in the eastern city.