The D.C. Council unexpectedly delayed a final vote Tuesday on regulating Airbnb and other short-term rental companies because of a last-minute dispute over how to pay for the legislation.

Chairman Phil Mendelson (D) reluctantly agreed to postpone what would be a final vote until Nov. 13 after council members David Grosso (I-At Large), Charles Allen (D-Ward 6) and Brianne K. Nadeau (D-Ward 1) raised objections in a testy debate.

The council unanimously gave preliminary approval to the bill two weeks ago. Since then, however, Mendelson and other supporters have been unable to satisfy concerns over an estimate from D.C. Chief Financial Officer Jeffrey S. DeWitt that the legislation would cost the city $104 million over four years.

Mendelson and council member Kenyan R. McDuffie (D-Ward 5), the bill’s original sponsor, expressed confidence that the financial issues could be addressed and that the bill would ultimately win approval with its main provisions intact.

“I am optimistic,” McDuffie said. “We’ll come back, and we’ll have the votes to get it passed.”

The proposal aims to impose some of the nation’s strictest limits on short-term rentals. It would prevent D.C. property owners from renting out second homes on a short-term basis and limit those who rent out spare rooms or basements in their primary residences.

It would affect thousands of D.C. property owners who have turned to “home sharing” to earn income, as well as the tourists and business travelers who use the service to find lodging in the nation’s capital.

Before postponing the matter, the council agreed to delay implementation, so if the law is passed, it would take effect Oct. 1, 2019. That would give the city time to create an enforcement and licensing agency, which would include 20 full-time employees.

The legislation has been pushed by the hotel industry and its unions, affordable-housing activists and community groups that argue short-term rentals are destroying the character of residential neighborhoods.

Airbnb has lobbied hard against the plan, saying it would cost property owners tens of millions of dollars in lost income. The company warned Monday it may seek to put the issue directly to voters with a ballot initiative in 2020.

Both sides have been running television ads and social-media campaigns to try to sway lawmakers and win public support.

Mayor Muriel E. Bowser (D) has suggested that she thinks the bill is too restrictive but has not threatened to veto it.

The vote was delayed primarily because of a dispute between Mendelson and DeWitt over how to calculate the bill’s impact and cost.

DeWitt warned Monday that the bill “is expected to eliminate nearly all current short-term rentals.”

That’s because he thinks passage of the bill would increase the chances that the city government would begin enforcing existing prohibitions on short-term rentals in residential areas, where as much as 90 percent of such rentals take place.

In a fiscal impact statement, DeWitt said the measure would cost the city $21.7 million in fiscal year 2019, and $104.1 million through fiscal year 2022, mostly from lost tax revenue if those short-term rentals are eliminated.

But Mendelson and his allies contend there’s no reason to believe the Department of Consumer and Regulatory Affairs is going to start enforcing zoning regulations that it has largely ignored.

“What will happen to the revenue? Over the next year, I would suggest, very little,” Mendelson said.

To assuage concerns, Mendelson offered to use surplus revenue to cover the bill’s future costs. But council members resisted that proposal, saying they didn’t want to commit funds that might better be used elsewhere.

Grosso expressed worry that the council was going to “be locked in to spend all this money, when I thought there were other ways to reduce” the cost.

“There are a whole mess of [other] very important programs that I would like to see revised revenue go to,” Nadeau said.

In the next month, Mendelson plans to try to persuade DeWitt to revise his estimate of the cost, or find another way to deal with the issue. He also has drafted a letter, which he expects many other council members to sign, asking the city zoning commission to permit short-term rentals. Sara Bardin, director of the D.C. Office of Zoning, declined to comment.

The debate over short-term rentals has become part of a broader controversy over gentrification in the District. Critics say Airbnb, HomeAway, VRBO and similar short-term-rental companies are driving up housing costs.

But Airbnb and its allies, including many hosts, argue that people living in the city need the extra income from renting out their properties to afford to stay in the District.

Home-sharing companies say the hotel industry and its unionized workers are trying to eliminate competition. About 9,000 short-term rentals operate in the District, competing with about 31,000 hotel rooms.

The rental companies say that short-term rental properties represent such a small fraction of the District’s 300,000 housing units that the overall effect on rents is minimal.