John McCain, who said Trump had "insulted every Russian citizen who was denied the right to vote in a free and fair election".
Sen. Lindsey Graham, a South Carolina Republican who is McCain's close friend but less publicly critical of Trump, echoed McCain's critique of Putin's re-election on Sunday without mentioning Trump.
In the aftermath of an election that appears to have had significant flaws, a prominent American critic of Putin - and of Trump himself - offered a stinging denunciation of the United States commander in chief's call.
'I had a call with President Putin and congratulated him on the victory, his electoral victory, ' Trump told reporters at the White House, referring to a race that the Russian strongman won with 77 per cent of the vote. 'What we do know is that Putin has been elected in their country, and that's not something that we can dictate to them, how they operate.
US President Donald Trump speaks during a round table meeting with members of law enforcement about sanctuary cities in the Roosevelt Room at the White House in Washington, on March 20, 2018. Senate Majority Leader Mitch McConnell said Trump "can call whomever he chooses" but noted that calling Putin "wouldn't have been high on my list".
The president and the White House Press office both provided official confirmation that the call took place, a day after the White House declined to describe the election as 'free and fair'. The administration also ripped Russia last week over allegations that Moscow was behind the poisoning of an ex-Russian spy with a military-grade nerve agent on British soil.
The White House responded to McCain's criticism on Tuesday, saying it is "important to have a dialogue with Russian Federation so we can focus on areas of shared interest".
"I don't believe it came up on this specific call but it is something that we have spoken extensively about and continue to look at ways and steps forward to make sure it never happens again", Sanders said of election meddling.
Rep. Ed Royce, R-Calif., chairman of the House Foreign Affairs Committee, implicitly rebuked Trump on Twitter, writing: "Putin does not deserve congratulations for his sham reelection". The United States has not taken similar action against Russian Federation for the attack, though the Trump administration last week sanctioned 19 individuals and five entities for their roles in the 2016 campaign meddling. The two did not hold a formal meeting, but they did informally talk a number of times during the two-day summit. Also, Putin's main opponent was blocked from the ballot.