HOUSTON — President Trump sided again on Tuesday with the government of North Korean leader Kim Jong-un in mocking Joseph R. Biden Jr.’s intelligence, an extraordinary alignment of a United States president and an authoritarian regime against an American politician — and an insult that Mr. Biden pooh-poohed by letting an aide rebut it.

During his visit to Japan last weekend, Mr. Trump wrote on Twitter that he had “smiled” when North Korea described Mr. Biden recently as a “fool of low I.Q.” The White House spokeswoman, Sarah Huckabee Sanders, also said that Mr. Trump and the Mr. Kim’s government “agree in their assessment” of Mr. Biden. American leaders have traditionally avoided partisan sniping while outside of the country.

Mr. Biden, who is running for the 2020 Democratic presidential nomination, did not respond to Mr. Trump’s remarks during his one public event on Tuesday, an education speech in Houston, or in response to reporters calling out questions afterward. At a fund-raiser in Houston Tuesday evening, Mr. Biden sought to stay above the fray, reaching for a line he has used to dismiss Mr. Trump in the past.

“I’m not going to get down in the mud wrestling with this fella,” Mr. Biden said. “I’m not going to do it. I don’t want to get into it. Everybody already knows who he is.”