Kremlin spokesperson Dmitry Peskov told reporters there had been speculation in the West about the president's health in recent months, but reports he was ill were "nothing but fakes".
Putin coughed during a public appearance on Wednesday, when Interfax news agency quoted him as saying he had caught a slight cold during a visit to Iran the previous day.
"It was very hot in Tehran yesterday, plus 38 (degrees Celsius), and the air conditioning was very strong there. So I apologise," Putin, 69, was quoted as saying.
International scrutiny of his health has intensified over recent months, including when he was photographed meeting foreign and Russian officials while seated at opposite ends of long tables as a precaution against COVID. At times he has also appeared to walk stiffly.
CIA Director William Burns was asked about the issue during a security forum in the United States on Wednesday, where he said that Putin was "entirely too healthy".