"Mr. Bush, not long ago you made the statement that the press in Russia is not free. What, in your view, is that lack of freedom all about?" Interfax reporter Alexei Meshkov asked.
Before Bush could answer, the reporter then turned on Putin and demanded to know why he was not sticking up for Russian reporters by talking about violations of the rights of American journalists.
A startled Bush then replied that Putin had brought up the subject of journalists getting fired recently in the United States.
"People do get fired in the American press. They don't get fired by the government, however. They get fired by their editors or they get fired by their producers or they get fired by the owners of a particular outlet or network," Bush said.
Under Putin, journalists who angered the Kremlin have lost their jobs, and television networks that challenged the Kremlin line have been taken over or shut down.
"If you're a member of the press corps and you feel comfortable with the press in Russia, then I think that is a pretty interesting observation for those of us who don't live in Russia to listen to," Bush said to Meshkov, whose news agency rarely deviates from the official line.
An equally agitated Putin rejected the notion he was keeping silent on the issue, but he said it was not something worth making a fuss about.
"What does it mean that we keep silent or I keep silent on some problems? First, I am not the propaganda minister," Putin said. "Second, we discuss all questions absolutely openly."