Trump has denied using the derogatory language.
Tillerson's remarks, which were planned earlier in the week and focused primarily on the need to prevent and address sexual harassment, highlighted a starkly different leadership style from the one employed by Trump, who has been known to use inflammatory language in describing his opponents.
The secretary of state began and ended his speech with the statement "values matter."
"Our values as a nation bond us together and define who we are" and "form the foundations of trust" in the workplace, he said.
"America's birth was far from perfect," said Tillerson, recalling the country's troubled past from its founding through the Civil War, the suffrage movement and the civil rights movement, "and we're still not perfect, but we've never lost sight of aspirational values."
Moreover, said Tillerson, "our lives are enriched when we recognize the diversity in our nation."
Tillerson drew loud applause from staff when he spoke of the need to end harassment at the State Department.
"No form of harassment is more demeaning than sexual harassment," he said. "Harassment and abuse have no place in a nation founded on the ideals of individual liberty and pursuit of happiness, and it can have no place at this organization, our State Department -- not here in Washington, not at posts abroad, nowhere."
"I cannot tolerate it, and I will not tolerate it," he said.