Haley has advocated such a test, citing Trump's age, 77 and Democratic President Joe Biden's age, 81.
Trump also insulted Haley with a demeaning nickname and accused her - a conservative Republican - of being "almost a radical left Democrat."
But much of his speech was focused on the southern border as Trump turned his attention to Biden. "We are going to seal the border, complete it, and we're going to repeal the invasion," Trump said.
Record numbers of migrants have been caught illegally crossing the U.S.-Mexico border since Biden took office in 2021, and opinion polls show immigration and the border as a top issue in this year's general election.
