WASHINGTON — President Trump added his former White House aide, Omarosa Manigault Newman, on Tuesday to the growing list of African-Americans he has publicly denigrated on Twitter, calling her “that dog” and a “crazed, crying lowlife” after her allegations against him of mental deterioration and racism.

Even for a president who consistently uses Twitter to assail his adversaries, the morning tweet about Ms. Manigault Newman was a remarkably crude use of the presidential bully pulpit to disparage a woman who once served at the highest levels in his White House.

In an interview on MSNBC, Ms. Manigault Newman responded that Mr. Trump treats women differently from men because he “believes they are beneath him” and that he talked in derogatory ways about minorities.

“He has absolutely no respect for women, for African-Americans,” she said.

In recent weeks, Mr. Trump has called Don Lemon, a CNN anchor, “the dumbest man on television.” He has questioned the intelligence of LeBron James, a star basketball player for the Los Angeles Lakers. And he has repeatedly said that Representative Maxine Waters, Democrat of California, has a “low I.Q.”