Graham joined Sen. Joseph Biden, D-Del., in urging the Bush administration to stand up to Putin. Their views reflect U.S. concerns over democratic backsliding by the Kremlin and the increasingly assertive steps by energy-rich Russia to counter American influence.
Graham cited President Bush's statement in 2001 that he got a sense of Putin's soul during the leaders' first meeting. "I think Bush misread his soul. I think this guy is taking Russia backward," Graham said.
"He's a problem, not a solution, to most of the world's problems. He could help us with Iran if he chose to. He is becoming basically a one-man dictatorship in Russia. And we need to be tough with him."
When asked about the death of an ex-KGB spy poisoned in Britain, Biden said he did not know if Putin was involved, "but our relations with Russia have to get straightened out to begin with."
"Russia is moving more and more toward an oligarchy here," Biden said. "We have basically been giving him a bye."
Biden, incoming chairman of the Senate Foreign Relations Committee, said he would consider "laying down markers about whether or not, as (Putin) continues to consolidate power within that economy and in that country ... he warrants continued membership" in the Group of Eight leading industrial nations.
The lawmakers spoke on "FOX News Sunday."