The Kremlin also denounced the rumors on Wednesday as “nothing but fakes.”
Dmitri S. Peskov, the Kremlin’s spokesman, told reporters that Mr. Putin was in good health and blamed “information specialists” from Ukraine, the United States and Britain for spreading rumors to the contrary.
Mr. Putin’s health was the subject of conjecture even before Russia invaded Ukraine in February. Unconfirmed rumors over the years have diagnosed the president — whose private life is largely shrouded in secrecy — with cancer, Parkinson’s disease, dementia and paranoia.
The war has also spurred rumors about the health of President Volodymyr Zelensky of Ukraine.
On Thursday, a Ukrainian radio station broadcast several statements claiming that Mr. Zelensky, 44, was in intensive care and that Ruslan Stefanchuk, the speaker of the Ukrainian parliament, had assumed the presidency.
The owners of the radio station later announced that the station had been hacked.
Mr. Zelensky addressed the rumor in a video speech, calling it fake news spread by Russia. He said he was speaking from his office and had never felt stronger.