WASHINGTON — President Obama and the first lady, Michelle Obama, issued scathing denunciations of Donald J. Trump on Wednesday, conveying the same message that a vote for a third-party candidate rather than Hillary Clinton would help elect a president who is unfit for office.

In a radio interview Wednesday morning, Mr. Obama lashed out at the Republican presidential nominee for denigrating women and mocked Mr. Trump’s debate appearance, saying it exposed him as a person who “appears to only care about himself.”

Mr. Obama described Mr. Trump as someone who was unqualified to sit in the Oval Office and “doesn’t do his homework, doesn’t know basic facts that you’d need to know.”

“You had somebody who basically insulted women and then doubled down,” Mr. Obama told Steve Harvey, a syndicated radio host. “In terms of how he talks about them and talks about their weight and talks about how they look instead of the content of their character and their capabilities, which is not something that I want, not somebody I want in the Oval Office.”