"Unfortunately, because of the fast pace of events, I inadvertently briefed the Vice President Elect and others with incomplete information regarding my phone calls with the Russian Ambassador. I have sincerely apologized to the President and the Vice President, and they have accepted my apology," Flynn continued.
Flynn had told Vice President Mike Pence he had not discussed U.S. sanctions against Russia with Russian officials in the weeks before Trump took office on Jan. 20, prompting Pence to defend him in subsequent television interviews.
In recent days, Flynn acknowledged he might have discussed sanctions with the Russians but could not remember with 100 percent certainty, which officials said had upset Pence, who felt he had been misled. Officials said Flynn apologized to Pence twice, including in person on Friday.
In the letter, Flynn thanked Trump for "his personal loyalty."
NBC reported that three candidates who could potential replace Flynn are Kellogg, Vice Adm. Bob Harward and retired Gen. David Petraeus.
Two senior U.S. officials told NBC News that Harward was considered the favorite.
Multiple outlets had reported earlier Monday that ousted acting Attorney General Sally Q. Yates warned the White House that Flynn might have been vulnerable to Russian blackmail.
Yates had delivered the message late last month amid worries about Flynn's communication with the Russian ambassador in Washington, according to The Washington Post, which cited unnamed current and former U.S. officials.
It wasn't clear, the Post reported, what White House Counsel Donald McGahn had done with Yates' information.
Yates was fired for opposing Trump's temporary entry ban for people from seven mostly Muslim nations.
In his resignation letter, Flynn wrote that, throughout his more than 30 years of military service and his brief tenure as national security advisor, he had "always performed my duties with the utmost of integrity and honesty to those I have served, to include the President of the United States."
—Reuters and CNBC staff contributed to this report.
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