"Absurd," Bannon told ABC News when asked about the reports.
The claim comes as multiple senior White House sources say Bannon did, in fact, threaten to quit his White House post after being informed that he was being removed from the elite team that crafts the administration's national security policy.
Sources tell ABC News that the move to take Bannon off the committee, which was implemented with little public fanfare this week, was "a long time coming" as part of an overhaul of the NSC by newly appointed national security adviser H.R. McMaster.
Until Wednesday, Bannon had been able to resist the changes, which sources said were part of a plan by McMaster to consolidate his authority and realign the NSC.
But in recent days, an already tense West Wing full of backbiting hit a new level of drama, as senior adviser Jared Kushner supported McMaster's move to remove Bannon, souring the once-close relationship between the president's ever-growing powerful son-in-law and Bannon.
Bannon, the sources said, appealed directly to President Trump, who was "stunned" when Bannon threatened to quit.
Bannon and his allies have sought to downplay the shake-up.
"Susan Rice operationalized the NSC during the last administration," Bannon said in a statement. "I was put on to ensure that it was de-operationalized. [National security adviser] Gen. McMaster has returned the NSC to its proper function."
A separate senior White House official corroborated Bannon's account, but would not go on the record.
"Steve was very instrumental in bringing on McMaster," the official said, casting Bannon's departure from the NSC not as a demotion but as a logical move. "Since McMaster basically shared his vision and view, there was no need for Steve to stay on."
A senior administration official says Bannon can still attend NSC meetings when he wants to, with the president's consent. Prior to Wednesday night's meeting, Bannon had only attended one NSC meeting. The official noted the lack of attendance further validates that Bannon's role was a temporary one.
ABC News' Shushannah Walshe contributed to this report.