Tillerson also distanced the State Department and the USA government from the president's response to a white nationalist rally in Charlottesville, Virginia, in which Trump blamed "both sides" for one death and 19 injuries there.
Speaking to Fox News host Chris Wallace, Mr. Tillerson said that that the State Department cherishes American values.
In the immediate aftermath of the events in Charlottesville, where several anti-racist counter-demonstrators were injured and one was killed, the USA became the subject of widespread global scrutiny and drew criticism from the U.N.'s Committee on the Elimination of Racial Discrimination.
Wallace asked Tillerson whether Trump's words in recent weeks had made it more hard to promote American values overseas.
Asked if this was the case also for "the values of the president", the head of american diplomacy, visibly uncomfortable, merely respond: "the president speaks for himself".
The top U.S. diplomat added that no one should harbor doubts that the United States government is committed to long-standing American principles.
Mr Trump triggered outrage earlier this month when he suggested both sides were at fault after unrest in Charlottesville in which a woman was killed when a white supremacist drove his vehicle into a group of counter-protestors.
Tillerson's remarks followed harsh criticism of Trump from National Economic Council Director Gary Cohn, who said in an interview Friday that he almost quit over the president's handling of the events in Charlottesville.More news: Record-breaking GCSE year for Markethill High
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Tillerson did not invoke Trump or levy direct criticism then, but his discussion of "hate speech" just days after the Charlottesville rally made his meaning clear.
Wallace mentioned the United Nations criticism in his question to Tillerson about Trump's comments.
"We do view it as a provocative act-a provocative act against the United States and its allies", Tillerson said, calling the firing "a violation of UN Security Council resolutions".
"It shows a lack of understanding of the President's broader policy when it comes to protecting Americans at home and overseas from all acts of terrorism", Tillerson said.
When Wallace asked if Tillerson was distancing himself from Trump's comments on Charlottesville, Tillerson said he shared his opinion in a State Department speech last week.
'Chris, we express America's values from the State Department, ' Tillerson answered.
North Korea has conducted more than a dozen missile tests this year, including two using ICBMS, sparking a war of words earlier this month between President Donald Trump and Kim's regime that rattled global markets. We represent American values, our commitment to freedom, our commitment to equal treatment to people the world over and that message has never changed.
The Administration "must do better in consistently and unequivocally condemning these groups", Cohn, who is Jewish, said. "So we condemn racism and bigotry in all its forms".