Nauert's comments are notably tougher on Russian Federation than those of the White House.
The report cited officials familiar with the call, who said that Trump allegedly chose to ignore the warning and also did not listen to aides who instructed Trump to condemn Russian Federation on using a nerve agent in the U.K. Trump also did not bring up Russia's meddling in the 2016 election, White House Press Secretary Sarah Huckabee Sanders told members of the press, CNN reported.
"We don't get to dictate how other countries operate", the press secretary, Sarah Huckabee Sanders, said.
But lingering controversies over the legitimacy of the Putin's election - and Putin's role in trying to undermine USA elections in 2016 - led to swift denunciations of the call. She says: "That's not simply what today's call was about".
"An American president does not lead the free world by congratulating dictators on winning sham elections", a statement issued by his office read.
But Russian elections aren't known for being fair or democratic; video shows ballot boxes being stuffed on Sunday, which resulted in at least 76 percent of the votes going to Putin.
Accusation of Putin role in poisoning is shocking
On Thursday, British Defense Secretary Gavin Williamson said Moscow had made a "deliberate political decision" to poison Skripal. Putin has so far only said publicly that Britain should get to the bottom of what has happened.
McCain has previously called Putin a murderer and a thug.
The flap comes as Donald Trump continues to fight off allegations that his campaign colluded with Russian Federation during the 2016 election.
President Donald Trump's National Security Council has drawn up a range of options should the President decide to take action against Russian Federation after the poisonings of a former spy and his daughter on United Kingdom soil, according to multiple State Department officials and a person familiar with the discussion.
Speaking to reporters at the White House during his meeting with Saudi Crown Prince Mohammed bin Salman, Trump confirmed: "I congratulated him [Putin] on the victory, the electoral victory". The election was tainted by reports of voting irregularities.
US President Donald Trump did not follow specific warnings from his national security advisers when he congratulated Russian President Vladimir Putin Tuesday on his reelection, including a section in his briefing materials in all-capital letters stating "DO NOT CONGRATULATE", according to officials familiar with the call.
The two leaders spoke out in favor of developing practical cooperation in various areas, including in ensuring strategic stability and combating global terrorism. And also to discuss Ukraine, and Syria and North Korea, and various other things. He also said they "will probably get together in the not-too-distant future" to talk about the global arms race and other mutual concerns, such as the war in Syria and North Korea's development of nuclear weapons.
Trump said Putin had made a statement that being in an arms race was not a great option and emphasised the importance of denuclearising the Korean Peninsula. His friend, the Chinese President Xi Jinping, has more than made-up for the lacklustre global response by terming his country's partnership with Russian Federation being at the "best level in history".