President Obama has concluded that the government must continue to play a significant role in the nation’s mortgage market, extending a federal loan subsidy for most homebuyers, according to people familiar with the matter.

Obama, who has promised a new vision for how the nation finances homebuying, has directed a small team to develop a proposal that would largely maintain the government’s role as an insurer of mortgages for most borrowers.

The proposal could even preserve Fannie Mae and Freddie Mac, the mortgage finance giants owned by the government, although under different names and with new significant constraints, said people knowledgeable about the discussions.

The president’s decision to preserve a major role for the government marks a big milestone in the effort to craft a new housing policy from the wreckage of the mortgage meltdown and could mean a larger part for Fannie and Freddie than administration officials had signaled.

If this approach became law, it probably would keep in place the kind of popular home loans that have been around for decades — 30-year fixed-rate mortgages with relatively low interest rates.

The plan is likely to draw criticism from many Republicans, who blame the financial crisis on policies they say overly encouraged the housing market. And many economists, including some who have worked in the White House under Obama, consider the federal role harmful to the free market.

The administration’s approach is still being sketched out, and no official decision on a proposal has been made. Officials have not determined whether to advance a final proposal before the 2012 presidential election. Officials from the White House, the Treasury Department and the Department of Housing and Urban Development are working out the details.

In a statement, the White House said it is premature to say that senior officials have agreed on any of the three main options outlined earlier this year in an administration white paper on reforming the housing finance system.

“It is simply false that there has been a decision to move forward with any particular option,” a White House official said. “All three options remain under active consideration and we are deepening our analysis around how each would potentially be implemented.”

The government could maintain a substantial role in various ways. These include restructuring Fannie and Freddie as public utilities overseen by a government regulator. The government would no longer guarantee their financial health, as in the past, but would continue to backstop the mortgage-backed securities they issue using loans made by private banks.

Or the two companies could be shut down altogether and replaced with several successors that, likewise, would have their mortgage-backed securities guaranteed by the government in exchange for a fee. A federal guarantee, by reducing the risk to investors, can make it cheaper for firms to raise money for making home loans, in turn reducing mortgage rates.

For years, Fannie and Freddie — shareholder-owned companies chartered by Congress to support the housing market — owned or insured trillions of dollars in home loans.

When the housing market crashed, the government seized the firms, and has spent more than $150 billion propping them up.