The flap with Britain started when Mr. Spicer, in the course of defending Mr. Trump’s original accusation against Mr. Obama, on Thursday read from the White House lectern comments by a Fox News commentator asserting that the British spy agency was involved. Andrew Napolitano, the commentator, said on air that Mr. Obama had used Britain’s Government Communications Headquarters, the signals agency known as the GCHQ, to spy on Mr. Trump.

The GCHQ quickly and vehemently denied the contention on Thursday in a rare statement issued by the spy agency, calling the assertions “nonsense” and “utterly ridiculous.” By Friday morning, Mr. Spicer’s briefing had turned into a full-blown international incident. British politicians expressed outrage and demanded apologies and retractions from the American government.