For more than a decade, four of the nation’s largest mortgage insurers paid millions of dollars in kickbacks to home lenders in exchange for business, raising insurance prices for consumers, the Consumer Financial Protection Bureau said Thursday.

The consumer watchdog agency fined Genworth Mortgage Insurance Corp., United Guaranty Corp., Mortgage Guaranty Insurance Corp. and Radian Guaranty Inc. a total of $15.4 million for an alleged scheme that the bureau said was a common practice in the lead-up to the nation’s housing meltdown.

“Illegal kickbacks distort markets and can inflate the financial burden of homeownership for consumers,” CFPB director Richard Cordray said.

Lenders typically require homebuyers who cannot afford a 20 percent downpayment on a house to buy mortgage insurance to offset the risk of default. The lender, not the borrower, selects the mortgage insurance company.

Those mortgage insurers often purchase their own insurance, known as “reinsurance,” to cover the risk of high losses on the mortgage.

At its peak in 2007, more than 15 percent of loan originations had private mortgage insurance, according to data from the Department of Housing and Urban Development.

The four mortgage insurance firms involved in the settlement bought reinsurance from subsidiaries of the lenders, an arrangement known as “captive reinsurance,” according to the CFPB. Government officials became suspicious because those firms’ reinsurance payments to the subsidiaries were much greater than the reinsurance that was provided, leading them to believe that the mortgage insurers were also paying the lenders to steer business their way.

“The mortgage insurance business can be lucrative, and our investigation indicates that lenders sought to leverage their control over the business to capture some of those revenues for themselves,” Cordray said.

Officials at the CFPB said they are investigating mortgage lenders who may have received kickbacks but declined to provide the number of or names of companies involved. The bureau also would not specify how much money the insurers paid lenders.

The CFPB inherited the case in July 2011 from the inspector general of HUD.

As part of the consent orders, which are subject to court approval, the four mortgage insurers will be banned from entering into any new captive reinsurance arrangements with affiliates of mortgage lenders for 10 years.

None of the insurers admitted any wrongdoing.

“We are pleased to put this behind us,” said Teresa Bryce Bazemore, president of Radian, in a statement. She said the company believed its reinsurance arrangements complied with federal law and “caused no harm to consumers” but agreed to the settlement “to eliminate distractions.”

The other firms involved in the settlement also maintain they were following the law and at no time deceived consumers. MGIC said homeowners were given the chance to opt out of captive reinsurance transactions. Genworth said that its borrowers paid the same for insurance regardless of whether they were part of a reinsurance arrangement.

Kent Markus, head of enforcement at the CFPB, said the four companies hit with enforcement orders are the only insurers writing policies today that had captive reinsurance arrangements in the time before the financial crisis hit.

“That’s crucial,” he said, “because the most important effect of today’s action will be to stop these practices in the marketplace and make sure they don’t restart as the housing market recovers in the coming years.”