The D.C. Council on Tuesday unanimously approved a broad tax on all health-related insurance products sold in the nation’s capital to solve a big money problem faced by its online health insurance exchange.

Under the measure, which will take effect on an emergency basis but eventually face congressional review, the exchange will fund its operating costs through a 1 percent tax on more than $250 million in insurance premiums paid annually by those who live and work in the District.

The taxable plans will include long-term care, disability, vision, dental, hospital indemnity and dozens of other health-related policies — almost all of which are not allowed to be sold on the exchange.

In warnings to city exchange officials, insurers who offer those products have threatened that the costs will be passed on to D.C. customers and that the exchange is certain to face a court challenge over whether it is overstepping the intent of Congress and the Affordable Care Act by taxing products not sold on the exchange.

Council member Muriel Bowser (D-Ward 4), the Democratic nominee for mayor, backed the tax but said she did not want to give the exchange a “blank check” to assess health plans ever-higher taxes to fund the exchange.

Council member David A. Catania (I-At Large), who is running for mayor as an independent, said that all health-related policies should be taxed regardless of whether they’re sold on the city’s exchange because they all benefit from a healthier public.

Like the 14 states that started online marketplaces, the District faces a year-end deadline to prove that its Web site can move past technology glitches and meet the looming challenge in President Obama’s Affordable Care Act: financial self-sufficiency.

But unlike the others, the city does not have enough customers buying insurance on its Web site to adopt the funding plan being employed by most states and the federal government — a tax of a few percentage points on premiums.

To cover its $28 million annual budget, the District’s exchange would have to levy a whopping 17 percent tax on every health plan sold on its Web site.

As an alternative, Mayor Vincent C. Gray (D) on Tuesday proposed legislation granting the District’s exchange board broad new power to tax any health-related insurance product.

Council member Yvette M. Alexander (D-Ward 7), chair of the Health Committee, said she would pursue funding for an annual audit of the exchange’s financing. She said she did not expect the assessment to exceed 1 percent.

“We don’t want it to be willy-nilly, and we want some money,” she said.

Insurers including Unum and Aflac had been among the most vocal opponents of the District’s plan. They argued unsuccessfully to exchange officials that their products — which in the event of a loss directly pay clients, not hospitals or doctors — are more financial-planning tools than health-insurance options.

They have also focused on broad language in the proposed legislation — “all health-insurance risks originating in or from the District” — to question if it could someday be used as the exchange’s prerogative to add a tax to life-insurance policies or medical portions of car insurance.

Mila Kofman, executive director of the exchange, said that is not the exchange’s intent and that the tax would hew closely to an established city program that does not tax those additional products.