"I had a call with President Putin and congratulated him on the victory, his electoral victory," Trump said later Tuesday. He added that the two leaders "will probably get together in the not-too-distant future" to discuss the international arms race.
Trump congratulated Putin even after aides, in briefing materials prepared ahead of the call, reportedly warned him: "DO NOT CONGRATULATE." Trump was also supposed to condemn the recent Russia-linked nerve agent poisoning of a former spy and his daughter in the U.K., but he did not, according to The Washington Post, which cited officials familiar with the call.
The phone call prompted a harsh response from some of Trump's biggest critics.
"An American president does not lead the Free World by congratulating dictators on winning sham elections," Sen. John McCain, R-Ariz., said in a statement condemning the call. "And by doing so with Vladimir Putin, President Trump insulted every Russian citizen who was denied the right to vote in a free and fair election."
The election win keeps Putin in office as Russia's president for another six years. His closest rival in the election, which was held Sunday, scored nearly 12 percent of the vote, while his most vocal opponent, Alexei Navalny, was barred from running in the race.
Putin's overwhelming victory and the circumstances leading to it have prompted criticism from Russia watchers. The White House, however, skirted the issue Tuesday.
"We're focused on our elections. We don't get to dictate how other countries operate," press secretary Sarah Huckabee Sanders said at Tuesday's White House press briefing. "What we do know is that Putin has been elected in their country."
Trump's comment on the arms race came as the top nuclear commander for the U.S. made a case Tuesday for America adding another nuclear weapon to its arsenal.
"I strongly agree with the need for a low-yield nuclear weapon," Air Force Gen. John Hyten, commander of U.S. Strategic Command, said of the Pentagon's request for a low-yield warhead for submarine-launched ballistic missiles.
"That capability is a deterrence weapon to respond to the threat that Russia in particular is portraying," he told the Senate Armed Services Committee on Tuesday.
Late last month, Putin made waves by boasting about an arsenal of new nuclear weapons, including an underwater drone, a new hypersonic missile and a cruise missile that has a "practically unlimited range."
Hyten has previously called Russia the "most significant threat" to the U.S. because the nation poses "the only existential threat to the country right now."
The call between Trump and Putin also comes as the special counsel's investigation into Russian meddling in the 2016 U.S. election intensifies. Trump has denied that his campaign colluded with Russia, and Putin has rejected accusations that the Kremlin had anything to do with any election interference.
The Trump administration announced last week that it was sanctioning several Russians and entities linked to the Kremlin for meddling in the 2016 election as well as for cyberattacks against U.S. infrastructure, such as the energy grid.
Trump had resisted calls to punish Russia for its malfeasance, despite U.S. intelligence agencies' claims that Kremlin-backed operatives did interfere in the campaign.
On Tuesday, Sanders told reporters Tuesday that she doesn't believe the subject of 2016 election meddling came up in the Putin-Trump phone call. "But it is something that we've spoken extensively about," she said.
Trump has expressed admiration for Putin dating back to the years before he ran for president, but he is not the only U.S. commander in chief to call the Russian leader after an election victory.
President Barack Obama called Putin in 2012 to congratulate him for his win that year, although Russia-U.S. relations were especially contentious during Obama's administration due in large part to the conflict in Syria. Russia has backed Syrian President Bashar Assad's brutal war.
Trump, for his part, has criticized Obama over his handling of the Syrian war. "President Obama said in 2012 that he would establish a 'red line' against the use of chemical weapons and then did nothing," Trump said in August after a suspected chemical attack in Syria. "The United States stands with our allies across the globe to condemn this intolerable attack."
The war in Syria continues to rage, and a Russian military leader recently threatened action against U.S. forces there if Americans target Russian servicemen.
— Reuters contributed to this report.