Kornelyuk, 37, and his television crew came under mortar fire while covering the political and military crisis in eastern Ukraine, the Organization for Security and Co-Operation in Europe (OSCE) said.
The Russian government news agency ITAR-Tass said he later died in a Luhansk hospital. Cameraman Viktor Denisov, who worked with Kornelyuk, survived the attack.
Russian Prime Minister Dmitry Medvedev, commenting on social media, said that "those who call themselves the authorities" in Ukraine were to blame for Kornelyuk's death.
"This death is yet another horrid reminder that not enough is being done to protect journalists who risk their lives reporting from conflict zones in Ukraine," said Dunja Mijatovic, the OSCE's representative on freedom of the media, who added the reporting crew's sound engineer, Anton Voloshin, remains missing.