WASHINGTON — Congressional bargainers have agreed to increase the size of mortgages insured by the Federal Housing Administration in a compromise being hailed by the housing industry but criticized by conservatives.

Under the deal by House and Senate negotiators, the FHA would be able to insure mortgages worth up to $729,750 in the most expensive regions of the U.S. for the next two years. The ceiling had been raised to that level during the financial crisis, but by law it dipped down to $625,500 on Oct. 1.

However, in a bow to conservatives, the bargainers would not increase the current $625,500 limit on mortgages that can be backed in expensive communities by Fannie Mae and Freddie Mac, the government-controlled mortgage giants, and by the Veterans Affairs Department.

Realtors and home builders had lobbied hard to raise the loan limits for all four entities, arguing that the last thing the country’s stubbornly weak housing market needs is stricter limits on government-backed mortgages. They were backed by members of Congress of both parties from areas where housing costs are high, like Southern California and New York.

“We’d have liked broader language, but the FHA is still an important part of the puzzle,” Jamie Gregory, a lobbyist with the National Association of Realtors, said Tuesday.

Conservatives and a majority of House Republicans oppose the increase, saying the government should reduce its involvement in subsidizing housing in hopes that the private market would step up.

The size of loans that federal agencies can back is based on a formula that includes a region’s median housing cost. More than a fifth of the country’s roughly 3,100 counties would be affected by the higher FHA loan limits.

FHA insurance is often used by buyers who put down small down payments. The agency has insured more than 40 million homes since it was established in 1934.

“FHA is important for first-time home buyers, so that will help support housing demand,” said Robert Dietz, an economist for the National Association of Home Builders.