Sen. Jeff Flake of Arizona, a frequent Trump critic, called the president's call "odd".
Trump's decision to congratulate Putin on his electoral win drew consternation from McCain who said that "an American president does not lead the free world by congratulating dictators on winning sham elections".
Mueller has reportedly sent questions to the White House for a potential interview with Trump, though Mueller and investigators remain tight-lipped and there is no official date on when Trump might sit with investigators for an interview.
In a statement about the call between the two leaders, the Kremlin described diplomatic problems facing Russian Federation and the US and confirmed Putin's intent to meet with Trump. Russian Federation denies interference in the election.
Trump supposedly ignored the order and called Putin on his own, the Washington Post reported on Tuesday.
Moment of silence held at FIU for bridge collapse victims
Southwest 8th Street remains closed indefinitely between 107th Avenue and 117th Avenue as crews work to clear the bridge debris. The 37-year-old died in hospital after being injured when the bridge collapsed onto a bustling roadway in Miami last Thursday.
Wigan vs Southampton TV channel, kick-off time, date and odds
Nathan Byrne linked up with Will Grigg after 14 minutes but the Northern Ireland worldwide dragged his shot wide from close range. Dusan Tadic's corner was stabbed goalwards by Hojbjerg and Wigan's Dan Burn couldn't react quick enough to clear off the line.
'Constructive talks': N Korean and Swedish foreign ministers meet
Its diplomatic mission in Pyongyang , which opened in 1975, was the first Western embassy established in the country. Sweden's prime minister told reporters on Saturday that the country stands ready to help "in any way".
"The leaders spoke out in favor of developing practical cooperation in various spheres including the issues of ensuring strategic stability and the fight against worldwide terrorism", the statement added.
"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 to determine their country's future, including the countless Russian patriots who have risked so much to protest and resist Putin's regime", McCain added.
"A special attention was given to considering the issue of a possible bilateral summit, " the Kremlin statement said.
The Kremlin said Tuesday's conversation between the two leaders had been broadly constructive and focused on overcoming problems in relations, which are at a post-Cold War low. He has also spoken about the need to avoid another arms race, despite using his pre-election address to showcase new Russian arms. Russian Federation has denied the allegations. They met on the sidelines of an global summit in Germany last summer and again more informally at another gathering of world leaders in Vietnam in November.
French President Emmanuel Macron and German Chancellor Angela Merkel made customary calls to Putin but voiced their grievances with the Kremlin's current domestic and foreign policies.
Meanwhile, critics laid into Trump earlier this month for his lukewarm response to the nerve-agent attack on former Russian military intelligence officer Sergei Skripal and his daughter Yulia, both of whom are now on life support.