The official noted that “there’s really not a lot of time — we’ve lost quite a bit of time that we would need” to prepare for the summit meeting.

“June 12 is in 10 minutes,” the official said.

On Friday, White House officials took pains to demonstrate that it was still possible to hold the meeting. Mr. Trump himself said Friday morning that he was hopeful again that there might still be a meeting on June 12 with the North Koreans.

“They very much want to do it,” the president told reporters. “We’d like to do it. We’ll see what happens.”

A recording of the key part of the Thursday briefing, discussing the timing issues of the summit meeting, appeared on Twitter after Mr. Trump’s tweet on Saturday. At the end of the briefing, reporters asked the official to put comments on the record, but the official said that both Mr. Trump and Secretary of State Mike Pompeo had spoken publicly, and that their comments could stand by themselves.

Mr. Trump’s attack on The Times was only the latest of many efforts by the president to discredit reporting by news organizations by questioning the validity of their sources.

On May 4, he attacked NBC News, saying in a tweet, “They cite ‘sources’ which are constantly wrong. Problem is, like so many others, the sources probably don’t exist, they are fabricated, fiction!” On April 21, he attacked The Times for an article on Michael D. Cohen, the president’s personal lawyer, saying that the newspaper used “non-existent ‘sources’ and a drunk/drugged up loser who hates Michael.”