Lindsey Graham said the only way Russia's invasion of Ukraine ends is "for somebody in Russia to take this guy out".
In a statement on Twitter, the outspoken Republican asks if the Russian president has a "Brutus" who can take out Mr Putin and end the war.
His comments have outraged the Russian ambassador to the US.
Mr Graham, who represents South Carolina, tweeted: "You would be doing your country - and the world - a great service.
"Is there a Brutus in Russia? Is there a more successful Colonel Stauffenberg in the Russian military?"
Brutus was a Roman politician who assassinated Julius Caesar, while German army Colonel Claus von Stauffenberg is best-known for trying to kill Adolf Hitler in 1944.
Anatoly Antonov, Russia's ambassador to the US, described his statement as "unacceptable and outrageous".
He said the degree of "Russophobia and hatred in the US towards Russia was off the charts.
"It's unbelievable that a country's senator preaching his moral values as a 'guiding star' to all mankind could afford a call on terrorism as a way to achieve Washington's goals on the international arena."
US President Joe Biden has condemned the Russian invasion and imposed sanctions on politicians including Mr Putin himself. He says the US will defend Nato countries but has ruled out sending troops to Ukraine.
And on Friday, White House press secretary Jen Psaki insisted Mr Graham's stance was "not the position of the United States government and certainly not a statement you would hear come from the mouth of anybody working in this administration".
Senator Graham's comments also riled Kremlin spokesman Dmitry Peskov.
"Of course, these days not everyone is managing to preserve a sober mind, I would even say a sound mind," he said, calling for national unity from Russians.