Lindsey Graham has attracted widespread condemnation after the South Carolina senator suggested Vladimir Putin should be assassinated in order to end Russia’s invasion of Ukraine.

Graham first made the suggestion in an appearance on Fox News host Sean Hannity’s show on Thursday evening, and he then repeated the idea in a tweet that quickly went viral.

“Is there a Brutus in Russia? Is there a more successful Colonel Stauffenberg in the Russian military? The only way this ends is for somebody in Russia to take this guy out,” Graham said on Twitter. “You would be doing your country – and the world – a great service.”

Brutus refers to one of the assassins of the Roman emperor Julius Caesar, and Stauffenberg was a German army officer who was executed for attempting to kill Adolf Hitler in 1944.

Graham added in a separate tweet: “The only people who can fix this are the Russian people. Easy to say, hard to do. Unless you want to live in darkness for the rest of your life, be isolated from the rest of the world in abject poverty, and live in darkness you need to step up to the plate.”

Despite immediate criticism of Graham’s comments from left and right in the US, he doubled down on the idea in a Friday morning interview with Fox & Friends. “I’m hoping somebody in Russia will understand that he is destroying Russia, and you need to take this guy out by any means possible,” Graham said.

Russian officials also attacked Graham’s comments as “criminal” and demanded that the US government provide an explanation for his rhetoric.

“The degree of Russophobia and hatred in the United States towards Russia is off the scale,” the Russian ambassador to the US, Anatoly Antonov, said in a Facebook post. “It is impossible to believe that a senator of a country that promotes its moral values as a ‘guiding star’ for all mankind could afford to call for terrorism as a way to achieve Washington’s goals in the international arena.”

American lawmakers of both parties responded to Graham’s comments with shock, dismay and outrage, pointing out the danger in demanding the assassination of a leader whose troops are currently engaged in shelling nuclear plants.

“I really wish our members of Congress would cool it and regulate their remarks as the administration works to avoid [a third world war],” the progressive congresswoman Ilhan Omar said in a tweet. “As the world pays attention to how the US and [its] leaders are responding, Lindsey’s remarks and remarks made by some House members aren’t helpful.”

The Democratic senator Brian Schatz added, “I have seen at least a half a dozen insane tweets tonight. Please everyone keep your wits about you.”

Republican members of Congress were no less critical, as Senator Ted Cruz derided Graham’s suggestion as “an exceptionally bad idea”. “Use massive economic sanctions; BOYCOTT Russian oil [and] gas; and provide military aid so the Ukrainians can defend themselves,” Cruz said. “But we should not be calling for the assassination of heads of state.”

Even Marjorie Taylor Greene – the extremist congresswoman who has sparked outrage for, among other things, comparing coronavirus-related restrictions to the treatment of Jewish people during the Holocaust – chimed in from the right with criticism of Graham.

“While we are all praying for peace [and] for the people of Ukraine, this is irresponsible, dangerous [and] unhinged. We need leaders with calm minds [and] steady wisdom,” Greene said on Twitter. “Not blood thirsty warmongering politicians trying to tweet tough by demanding assassinations. Americans don’t want war.”

Experts in Russian politics argued that Graham’s suggestion was not only irresponsible but also unrealistic. Bill Browder, the financier whose work against Russian corruption led to the Magnitsky Act of 2012, described Putin as “probably the most paranoid man in the world”.

“He’s a very little man. He’s very scared of everybody, and he’s very vindictive. And so he’s constantly looking around for betrayal,” Browder told CNN on Friday. “I don’t think that there’s going to be a palace coup because he’s looking to try to stop it.”

At the daily White House media briefing, the White House press secretary, Jen Psaki, said: “We are not advocating for killing the leader of a foreign country or regime change. That is not the policy of the United States.”