"In 2003 I warned of a 'creeping coup' in Russia against the forces of democracy and market capitalism in Russia," said McCain, who ran for the Republican presidential nomination in 2000, which he lost to Bush.
"Since then, Russia has actually moved backward," he said.
"Mr Putin has moved to eliminate the popular election of Russia's 89 regional governors, has cracked down on independent media, continued his repression of business executives who oppose his government, and is reasserting the Kremlin's old-style central control," McCain added.
"The coup is no longer creeping - it is galloping," the Arizona senator said.
Lieberman, who ran for the Democratic presidential nomination last year, said: "We must openly confront anti-democratic backsliding in Russia for the sake of all those who look to the United States as a beacon of freedom."
The G8 also includes the United States, Britain, Canada, Japan, France, Italy and Germany.