President Trump’s remarks on Friday that he would not rule out a “military option” to quell the chaos in Venezuela set off a late-night diplomatic duel, with the defense minister accusing Mr. Trump of “an act of madness” and the White House saying it had turned away a call from Venezuela’s president.

“It is an act of supreme extremism,” Defense Minister Vladimir Padrino López said late Friday in Caracas, the capital.

“As our minister of defense and a Venezuelan citizen,” he added, “I say it is an act of madness.”

About an hour later, the White House issued a statement saying that Mr. Trump had refused to take a phone call on Friday from Venezuela’s president, Nicolás Maduro.

“Today, Nicolas Maduro requested a phone call with President Donald J. Trump,” the White House said. “President Trump will gladly speak with the leader of Venezuela as soon as democracy is restored in that country.”