Naming Senate Majority Leader Mitch McConnell and House Speaker Paul Ryan specifically, Bannon told CBS's Charlie Rose: "They do not want Donald Trump's populist, economic nationalist agenda to be implemented. It's very obvious."
Bannon recalled a meeting with McConnell in Trump Tower, when the Kentucky Republican asked Trump to clamp down on his "drain-the-swamp" rhetoric.
"Oh, Mitch McConnell when we first met him, I mean, he said -- I think in one of the first meetings in Trump Tower with the President -- as we're wrapping up, he basically says, 'I don't want to hear any more of this 'drain-the-swamp' talk,'" Bannon recalled. "He says, 'I can't -- I can't hire any smart people,' because everybody's all over him for reporting requirements and -- and the pay, et cetera, and the scrutiny. You know, 'You gotta back off that.'"
Asked about attacking the very people Trump needs to enact his agenda, Bannon said GOP leaders won't provide such help "unless they're put on notice."
"They're going to be held accountable if they do not support the President of the United States," he said. "Right now there's no accountability. ... They do not support the President's program. It's an open secret on Capitol Hill. Everybody in this city knows it."
Neither McConnell nor Ryan's offices immediately responded to CNN requests for comment about Bannon's remarks.
Bannon criticized the House and Senate leadership for what he said was their overpromising and underdelivering on health care, saying they told the White House that they would repeal and replace Obamacare in the first few months of the administration and the new Congress before moving on to a tax overhaul by summer and infrastructure legislation by year's end -- none of which, as of yet, has happened.
While Bannon said he does not entirely blame the Republican leaders for their inability to move such major legislation, he said they were unaware of the divisions within their own party.
"There is wide discrepancy in the Republican Party, as we know today, now that we're in it," Bannon said. "But I will tell you, leadership didn't know it at the time. They didn't know it 'til the very end."
Bannon was ousted in mid-August amid a reshuffling of power within the White House, just a few weeks after retired Marine Corps Gen. John Kelly took over as chief of staff with a goal of instilling order in a chaotic operation beset by internal divisions, staff infighting and a storm of controversies.
Bannon has since returned to his role as executive chairman at the conservative online publication Breitbart News, a job he held before joining Trump's campaign. Sunday's interview is the first time has spoken out publicly since his firing.
His exit meant one of the White House's most controversial staffers, the man generally perceived as the driving force behind Trump's "nationalist" ideology, would no longer be at the center of the Trump universe.