Trump has done little to encourage unity in recent days, instead inflaming tensions with his critics through a series of tweets. The incoming president tweeted Saturday that Lewis should pay more attention to his "crime ridden" Atlanta-area district, adding that the civil rights leader was "all talk."
Lewis suffered a fractured skull when he led a march in Selma, Alabama, more than a half century ago and has devoted his life to civil rights.
The current White House chief of staff, Denis McDonough, said "Lewis has literally fought, bled and gone to jail" during what he called his "remarkable life." He encouraged the incoming president to move past Lewis' criticism.
"That would be the kind of thing that would not only send a message to the American people that we're prepared to work together, but would also send a message to the Russians that we are united," McDonough said on CNN's "State of the Union."
Questions about Trump's relationship with Russia have dominated the days leading up to his inauguration.
Ret. Gen. Michael Flynn, who is set to become Trump's national security adviser, has been in frequent contact with Russia's ambassador to the U.S. in recent weeks, including on the day the Obama administration hit Moscow with sanctions in retaliation for the alleged election hacking, a senior U.S. official said.
After initially denying the contact took place, Trump's team publicly acknowledged the conversations on Sunday.
"The conversations that took place at that time were not in any way related to the new U.S. sanctions against Russia or the expulsion of diplomats," said Vice President-elect Mike Pence, also in an appearance on "Fox News Sunday."
Repeated contacts just as Obama imposed sanctions would raise questions about whether Trump's team discussed - or even helped shape - Russia's response. Russian President Vladimir Putin unexpectedly did not retaliate against the U.S. for the sanctions or the expulsion of 35 Russian diplomats, a decision Trump quickly praised.
Trump has repeatedly called for a better relationship between the U.S. and Putin's government. He suggested in an interview with the Wall Street Journal on Friday that he'd consider easing the latest sanctions on Russia.
"I think he has to be mindful that he does not have a full appreciation and understanding of what the implications are of going down that road," Brennan said.
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