WASHINGTON—Republican vice presidential nominee Mike Pence on Wednesday endorsed Paul Ryan in his primary race, a day after Donald Trump kicked off a new GOP firestorm by withholding support from the House speaker.

“I strongly support Paul Ryan, strongly endorse his re-election,” said Mr. Pence in a phone interview with Fox News. He added that the presidential nominee supported his decision to back Mr. Ryan, with whom Mr. Pence had served in the House.

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