The comments were contained in a memo as the Office of Management and Budget (OMB) was directed to crack down on spending relating to learning about subjects such as white privilege.
OMB director Russell Vought asked federal agencies to identify spending related to any training on “critical race theory” or any other material that teaches or suggests that the United States or any race or ethnicity is “inherently racist or evil”.
The memo comes as the country has faced a reckoning this summer over racial injustice in policing and other spheres of American life.
Mr Trump has spent much of the summer defending the display of the Confederate battle flag and monuments of Civil War rebels from protesters seeking their removal, in what he has called a culture war” ahead of the November 3 election.
Meanwhile, he has rejected comments from Democratic nominee Joe Biden and others that there is “systemic racism” in policing and American culture that must be addressed.
Mr Vought’s memo said additional federal guidance on training sessions is forthcoming, adding: “The President, and his Administration, are fully committed to the fair and equal treatment of all individuals in the United States.
“The President has a proven track record of standing for those whose voice has long been ignored and who have failed to benefit from all our country has to offer, and he intends to continue to support all Americans, regardless of race, religion, or creed.
“The divisive, false, and demeaning propaganda of the critical race theory movement is contrary to all we stand for as Americans and should have no place in the Federal government.”