TheGatewayPundit.com, a right-wing site, called it a “notorious” interview and said it proved Obama administration officials had disseminated “intel gathered on the Trump team.” Reince Priebus, the White House chief of staff, said on the Hugh Hewitt radio show that Ms. Farkas had made “just an incredible statement.” Breitbart News reported on Mr. Priebus’s comments.

The comments by Ms. Farkas, Mr. Spicer said, were evidence that Mr. Trump or his associates “were surveilled, had their information unmasked, made it available, was politically spread.” He said that such stories were proof that Obama administration officials had “misused, mishandled and potentially did some very, very bad things with classified information.”

In fact, the reports do not back up the allegations that Mr. Trump or any officials in his campaign were ever under surveillance. In the March 2 interview on MSNBC’s “Morning Joe” program, Ms. Farkas said she had expressed concern to her former colleagues about the need to secure intelligence related to the Russian hacking of the American election.

Ms. Farkas was commenting on a New York Times article a day earlier that documented how in the days before Mr. Trump’s inauguration, Obama administration officials had sought to ensure the preservation of those documents in order to leave a clear trail for government investigators after Mr. Trump took office.

In a statement she gave to The American Spectator, a conservative publication, Ms. Farkas said the furor over her remarks was “a wild misinterpretation of comments I made on the air in March.” She added, “I was out of government, I didn’t have any classified information, or any knowledge of ‘tapping’ or leaking or the N.Y.T. article before it came out.”

White House officials also confronted on Friday the disclosure that Mr. Flynn, who resigned in February over his contacts with Russian officials, has offered to testify before the two congressional committees investigating the Trump campaign’s ties to Russia about those contacts in exchange for immunity from prosecution.

Mr. Trump said on Twitter on Friday morning that he agreed with Mr. Flynn’s proposal.

“Mike Flynn should ask for immunity in that this is a witch hunt (excuse for big election loss), by media & Dems, of historic proportion!” Mr. Trump wrote.