“We’re in front of a very hostile judge,” Mr. Trump said. “The judge was appointed by Barack Obama, federal judge. Frankly, he should recuse himself because he’s given us ruling after ruling after ruling, negative, negative, negative.”

Mr. Trump also told the audience, which had previously chanted the Republican standard-bearer’s signature “build that wall” mantra in reference to Mr. Trump’s proposed wall along the Mexican border, that Judge Curiel is “Mexican.”

“What happens is the judge, who happens to be, we believe, Mexican, which is great. I think that’s fine,” Mr. Trump said.

Judge Curiel was born in Indiana.