"I'm not particularly concerned about all of this," McConnell said. "I refuse to get diverted off on the various comments that may be made at one time or another."
Trump and allies, including Bannon, had previously blamed McConnell for stalling health care and other legislation.
McConnell insisted that the confirmation of Justice Neil Gorsuch and other Trump nominees for executive and judicial positions was indicative of the Senate doing its job to support Trump's legislation.
"The kind of people who are supported by the element that you've just been referring to are specialists in defeating Republican candidates in November," McConnell said. "And that's what this inter-party skirmish is about. Our goal is to nominate people in the primaries next year who can actually win, and the people who win will be the ones who enact the president's agenda."
McConnell said Bannon and other anti-establishment backers have caused the GOP to lose senate seats in recent years.
"They've been out there for a number of years," he said. "They cost us five Senate seats in 2010 and 2012. We would have got the majority sooner but for the fact they were able to nominate people who could not win in November. In '14 they were defeated everywhere, in '16 they were defeated everywhere, and the difference is we've been in the majority in 2014 and 2016, two congresses in a row."