President Trump on Saturday claimed The New York Times quoted a "'senior White House official' who doesn't exist." "Use real people, not phony sources," Mr. Trump tweeted.

But reporters listened to that official, in person and on the phone, on Thursday during a White House-sanctioned background briefing.

CBS News is not publishing the name of the White House official, as the ground rules for the background briefing called for keeping the official anonymous. The official was asked to put the name on the record, but that request was denied.

The Failing @nytimes quotes “a senior White House official,” who doesn’t exist, as saying “even if the meeting were reinstated, holding it on June 12 would be impossible, given the lack of time and the amount of planning needed.” WRONG AGAIN! Use real people, not phony sources. — Donald J. Trump (@realDonaldTrump) May 26, 2018

In his tweet Saturday, Mr. Trump quoted a portion of a New York Times article that referred to what the official had said. What the president quoted was not a direct quote of the official, but rather The New York Times' paraphrasing of the official's comments on an anticipated -- then canceled -- June 12 summit between President Trump and North Korean leader Kim Jong Un. The paper reported that "a senior White House official told reporters that even if the meeting were reinstated, holding it on June 12 would be impossible, given the lack of time and the amount of planning needed."

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While the official didn't use the word impossible, the official said, when asked if a June 12 summit would still be possible, that there's "really not a lot of time" to make that happen, and "June 12th is in 10 minutes."

"There's really not a lot of time," the official told reporters Thursday afternoon. "We've lost quite a bit of time that we would need in order to — I mean, there's been an enormous amount of preparation that's gone on over the past few months at the White House, at State, and with other agencies and so forth. But there is a certain amount of actual dialogue that needs to take place at the working level with your counterparts to ensure that the agenda is clear in the minds of those two leaders when they sit down to actually meet and talk and negotiate and hopefully make a deal. June 12th is in 10 minutes and the president has said that someday he looks forward to meeting with him."

The president has offered different messages on North Korea since canceling the summit, most recently indicating it might still happen on June 12.

"We are having very productive talks with North Korea about reinstating the summit which, if it does happen, will likely remain in Singapore on the same date, June 12th, and if necessary, will be extended beyond that date," the president tweeted Friday night.

We are having very productive talks with North Korea about reinstating the Summit which, if it does happen, will likely remain in Singapore on the same date, June 12th., and, if necessary, will be extended beyond that date. — Donald J. Trump (@realDonaldTrump) May 26, 2018

This isn't the first time the president has accused the media of making up sources.

In a radio interview last month, for instance, the president explained why he would be skipping the White House Correspondents' Dinner.

"I sort of feel that the press is so bad," Mr. Trump said at the time. "It's so fake, it's so made up. I mean, 'sources say' and they have no sources. They're like novelists. I call them novelists."

— CBS News' Jacqueline Alemany contributed to this report.