Washington (CNN) Secretary of State Rex Tillerson said Sunday that President Donald Trump "speaks for himself" when asked whether the President's response to the violence in Charlottesville, Virginia, raised questions about Trump's values.

The brief remark from the top Cabinet official appeared to be the latest subtle sign of a gap between Tillerson, a former globe-trotting oil executive, and the freewheeling President, who ran a campaign in large part against how the US interacts with pillars of the international community.

It also points to a distance between Trump and some of his team on Charlottesville.

Tillerson said on "Fox News Sunday" that the United States was committed to freedom and "equal treatment of people the world over" when posed the question by anchor Chris Wallace.

"I don't believe anyone doubts the American people's values," Tillerson said.

"And the President's values?" Wallace asked.

"The President speaks for himself," Tillerson said.

Tillerson's comment was in response to a line of questioning about a United Nations committee issuing a warning to the United States about racism and hate crimes, saying US leaders had not sufficiently condemned white supremacy. Trump was widely criticized for his response to the racially motivated violence in Charlottesville, in which he said "both sides" -- white supremacists and those protesting them -- were responsible for the clashes that left one woman dead and dozens injured.

Trump initially blamed the violence on "many sides," but amid mounting criticism, he called out white supremacists and hate groups like the Ku Klux Klan specifically a couple of days later. Then, the next day, he generated further controversy with his "both sides" remark during a press conference at Trump Tower.

The White House did not immediately respond to a request for comment on Tillerson's remarks, and the State Department said it would get back to CNN if there was "anything to share."

'My own comments'

Tillerson's comment followed a curious line from Defense Secretary James Mattis about problems in the US that he said had not manifested themselves in the military.

Speaking to service members in a video picked up by The Guardian , Mattis said, "Our country right now, it's got problems we don't have in the military."

"You just hold the line until our country gets back to understanding and respecting each other and showing it," Mattis said.

And Gary Cohn, the director of Trump's National Economic Council, reportedly mulled resignation after Trump's response to Charlottesville, people familiar with the situation told CNN. Cohn stayed, but he told the Financial Times that the administration "can and must do better" on condemning hate groups.

In the Fox interview with Tillerson, Wallace asked if he was trying to distance himself from Trump explicitly.

"Are you separating yourself from that, sir?" Wallace continued.

"I made my own comments as to our values as well in a speech at the State Department last week," Tillerson replied.

In that speech earlier this month, Tillerson delivered a condemnation of both hate and those who "protect or accept hate speech" in any form -- a sharp contrast with some of the comments made by Trump.

"It's simply important to say -- although I think it's well understood and embraced, I'm certain, by everyone in this room -- we all know hate is not an American value, nowhere is it an American value," the top US diplomat said.

In the past, Tillerson has come under fire for saying, as he did in May, that US foreign policy should sometimes separate values such as freedom, human dignity and "the way people are treated" from policies it pursues around the world.

Reports of differences

In the interview on Sunday, Tillerson denied an ongoing fight in the administration was occurring between "nationalists" like the recently departed Steve Bannon and "globalists," referring to people who advocate for increased international cooperation and free trade. But in practice, Tillerson's State Department has found itself on occasion grappling with both the President's words and aides seeking to steer foreign policy.

Just months into the job, the difficulties for Tillerson played out on the world stage -- from his attempt to mediate the Gulf region's dispute over Qatar's alleged involvement in terrorism being reshaped by tweets from the President, to the former Exxon Mobil chief's inability to sway Trump on staying in the Paris climate agreement.

Tillerson did not attend the speech in which Trump made his decision on the Paris agreement public, and the State Department did not say why the nation's top diplomat was not present for the announcement of a major foreign policy move.

For his part, Tillerson downplayed the significance of the decision Trump had treated with so much fanfare.

Differences between Tillerson and Trump became further pronounced when reports suggested he was mulling stepping down from the job. Then Tillerson took an unannounced vacation in July, and State Department spokesperson Heather Nauert declined to say if the secretary was happy with his role.

When Tillerson came back, he said his relationship with Trump was "good" and that he would stay on the job as long as Trump let him.