He said that at the end of 2018, only 11 credit unions had assets of more than $10 billion—the threshold for CFPB authority. That follows a July 2017 letter from then-NCUA Chairman J. Mark McWatters to former CFPB Director Richard Cordray asking the director to cede examination and enforcement provisions of Dodd-Frank.

In their letter, the banking groups said that Nussle's letter is the latest seeking exemptions from CFPB rules based solely on an institution's charter type.

"The credit union industry is not small, special, or immune to the consumer risks the Bureau is charged by Congress to address," the bankers said, adding that credit unions "trumpet" that they are no different than banks when it is convenient to do so.

Congress was clear when enacting Dodd-Frank that credit unions should be subject to the law, the bankers said.

And they contend that questions have been raised about the NCUA's supervisory role, citing an agency Inspector General report that said that examiners could have mitigated losses at credit unions heavily invested in the taxi industry if they had taken action sooner.

The bankers said that credit union advocates should stop trying to unfairly benefit themselves by creating a competitive advantage by placing themselves outside CFPB authority.

"We urge the Bureau to reject the self-serving call for credit unions to be treated differently than other lenders," the letter concludes.