A broad new tax to fund the D.C. health exchange is unconstitutional and the city should be barred from collecting it, according to a complaint filed Thursday in federal court by a national insurance industry group.

The lawsuit alleges that the tax recently approved to prop up the D.C. exchange — one of the nation’s costliest per enrollee — will drive up premiums for residents on dozens of insurance products that receive no benefit from the exchange.

In its filing in U.S. District Court, the American Council of Life Insurers calls the arrangement an illegal taking under the Fifth Amendment as well as a violation of the Affordable Care Act, which calls for state-run exchanges to be financially self-sufficient by the end of the year.

“We have a number of constitutional claims that all point in the same direction,” said Paul D. Clement, a former U.S. solicitor general under President George W. Bush, who is representing the insurers.

“Governments have a lot of freedom to impose taxes on the general population, but what they don’t have is the ability to make one group of people pay for something that they don’t get some benefit from.”

A spokeswoman for the D.C. Health Exchange declined to comment, but officials have previously defended the plan, saying that everyone benefits when more residents are insured.

Like the 14 states that started online marketplaces with funding from President Obama’s health-care law, the District has been grappling with an array of problems, including how to pay for the marketplace’s ongoing cost. Unlike the others, the city does not have enough customers buying polices to copy the funding strategy that most states and the federal government adopted: a tax of a couple percentage points on medical plans sold on exchanges.

A study recently pegged the D.C. exchange’s cost per enrollee at nearly $12,500, second only to Hawaii. D.C. exchange officials warned that to cover costs, a whopping 17 percent tax would be needed on every plan issued on the D.C. Health Link Web site. The leading insurers who offer plans on the Web site cautioned that such a tax could erase many low-income residents’ benefits of buying plans through the exchange.

As an alternative, exchange officials proposed spreading out the cost by taxing insurance products beyond those offered on the exchange: all health-related policies issued annually in the District. Mayor Vincent C. Gray (D) and the D.C. Council agreed.

Exchange officials have said they would soon begin collecting the 1 percent tax on long-term care, disability, vision, dental, hospital indemnity and dozens of other policies.

In all, in fact, the majority of the D.C. exchange’s roughly $28 million budget would be funded by taxes on products not sold on its Web site.

Insurers including Unum and Aflac have been among the most vocal opponents. They argue that their products — which in the event of a loss pay clients directly, not hospitals or doctors — are more financial planning tools than health insurance options.

“By seeking to fund the operation of the D.C. Exchange in this manner, the District is seeking to obligate certain companies to endow a State-sponsored marketplace for the exclusive use of a small subset of health insurance issuers,” read the complaint filed Thursday, which among others names Gray and Mila Kofman, the exchange’s executive director.

Kofman could not be reached Thursday to comment, but during the spring, while lobbying Gray and others to back the plan, she said that issuers of all affected policies would benefit from a well-running D.C. exchange — namely, a healthier society that cashes in on policies less often.

But Kofman also acknowledged that the District had no choice: “No other state needs to do this because they have a higher population,” Kofman said. “We are in a unique situation.”

Two states have smaller populations than the District: Vermont and Wyoming. Vermont is paying for its exchange in part by raising rates on paid insurance claims. Wyoming is utilizing the federal exchange, which charges insurers 3.5 percent of premiums collected on plans sold on the exchange.

In its complaint, the ACLI said the District’s unique need doesn’t give it the right to override the Affordable Care Act, which grants states the right to fund exchanges only through fees and levies on products sold on exchanges.

In a statement, Gary Hughes, executive vice president and general counsel of ACLI, which represents 300 insurers, stressed that the group isn’t trying to pick a fight with the Affordable Care Act.

“Our concerns are solely focused on how D.C. has chosen to fund its own exchange,” Hughes said. “Because these products are prohibited from even being sold on the exchange, the supplemental insurance carriers would be paying an assessment without seeing any benefit. In addition, the cost of the assessments will likely, and unfairly, impact the affordability of these products for consumers in the District of Columbia.”