Scott attracted both praise and criticism when he said Mr. Trump "compromised" his "moral authority" in blaming "both sides" for violence in Charlottesville, saying there were "very fine people" among the white nationalist protesters.
"We hope that President Trump will move quickly to sign this resolution and commit his Administration to address the rise of hate groups", said Virginia's Democratic Senators Mark Warner and Tim Kaine, who sponsored the resolution.
White House Press Secretary Sarah Huckabee Sanders said Trump "looks forward" to putting his name on the document once it lands on its desk, which should happen soon.
While it's not uncommon for resolutions to go through the House and the Senate, it's rare that they head to the President for signature.
The one-on-one meeting Wednesday at the White House is also an effort by the president to unify the country.
"My response was, while that's true - if you look at it from a sterile perspective, there was an antagonist on the other side - however, the real picture has nothing to do with who's on the other side", Scott continued.
Sanders - who attended the meeting with Vice President Mike Pence, White House legislative affairs director Marc Short, deputy legislative affairs director Mary Elizabeth Taylor and Scott's chief of staff Jennifer DeCasper - called the meeting constructive.
While some people said the issue was a "petty" one to point out, one person said: "I don't think we're asking too much for him to dress like a president". "Tom Scott" in the caption of the original White House photo of the meeting.
After his presidential one-on-one, Scott said it was those same themes that drove him to ask for a meeting with the president. During his speech, Trump equated the actions of White supremacists to those who were protesting them.
When asked if Scott had expressed his "displeasure" at the president's response to Charlottesville, she said, "Not at all", adding that Scott and Trump had discussed "what we can do to bring people together, not talk about divisions within the country". "What I wanted to get out of the conversation was a focus on fairness and opportunity", the senator also told CBS News. "I do not know many African American men who do not have a very similar story to tell, no matter their income, no matter their disposition in life".
On Thursday, speaking to reporters on Air Force One, Mr. Trump reverted to the unapologetic stance he took in a news conference last month at Trump Tower.