Dowd told ABC News he wrote those words. A second source who corroborated that Dowd had written the tweet called it "sloppy."
It's unclear who actually sent out the tweet, but Dowd said he gave the drafted message to the president's social media director Dan Scavino.
"I’m out of the tweeting business," Dowd said. "I did not mean to break news."
The White House, which has insisted that tweets from the president should be taken as official statements, has declined to comment.
The apparent admission made in the president's tweet -- that he knew Flynn had lied to the FBI at the time of his firing -- would seem to add a potentially explosive new dimension to the ongoing special counsel investigation.
While Dowd concedes that Deputy Attorney General Sally Yates informed White House Counsel Don McGahn in January following Flynn's interview with the FBI that "the agents were told the same thing the Vice President was told," he maintains that the president did not know Flynn had lied to the FBI because the Department of Justice did not characterize Flynn as having lied.
"The FBI and Yates and the Department of Justice did not accuse Flynn of lying despite the fact that he lied to the agents, but nobody was accused of it, so the president didn't know about it," Dowd said.
"All the president knew was that the department was not accusing him of lying," Dowd later added.
Administration officials have declined to comment on that matter and the president did not respond to shouted questions Saturday evening about Flynn's firing as he returned home from campaign fundraisers in New York City.
Editor’s note: An earlier version of this story indicated Dowd referred to the tweet as "sloppy." It was a second source who corroborated Dowd’s account who also called it "sloppy."