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“I think that there should have been coordination, especially when you are taking on the president of the United States,” he said.

A spokesman for the Department of Insurance, Securities and Banking declined to comment as did a spokesman for the city’s Health Benefit Exchange Authority.

Mr. White and Washington state Insurance Commissioner Mike Kreidler were among the first regulators to raise concerns Thursday about the president’s decision to delay enforcement of the Affordable Care Act’s minimum coverage standards that require insurers to cover a range of services and scrap coverage that the law’s supporters viewed as substandard.

The warnings came on top of concerns from America’s Health Insurance Plans President Karen Ignani, who said “changing the rules after health plans have already met the requirements of the law could destabilize the market and result in higher premiums for consumers.”

District lawmakers said the city’s health exchange has run smoothly since opening. D.C. Council Chairman Phil Mendelson framed Mr. White’s dismissal as an unnecessary distraction.

“What the former insurance commissioner said was similar to what has been said by other state insurance commissioners,” Mr. Mendelson, a Democrat, said. “So it would have just blended into the background with that.”

As of Wednesday, the exchange authority reported that 19,706 accounts had been created on its website and 1,350 applications for full-price coverage had been completed.

“The city did well in setting up D.C. Health Link and we were one of the ones that successfully implemented our program,” Mr. Orange said. “Now we have to see how we will work to reconcile with the president’s new pronouncement.”