It’s a rare area of agreement between Republicans and the Obama administration: The government should reduce its outsize role in making sure that people can buy homes.

And yet, in the past three months, these officials and others in Washington have taken steps that expand the government’s support of the housing market.

The reason is that the economy and the housing market, in particular, remain weak. Officials are worried that withdrawing government support for housing could make it more difficult for people to buy homes, reducing demand and sending housing prices even lower.

In September, the Federal Reserve announced it would resume purchasing mortgage investments, which flood the mortgage markets with money and reduce interest rates on home loans.

In October, the Obama administration joined with federal regulators to announce a new plan to enable more “underwater” borrowers, who owe more on their loans than their properties are worth, to refinance at today’s low rates if they have government-backed loans.

And this month, Congress and President Obama signed off on a bill that would increase the size of a mortgage that borrowers can obtain from the Federal Housing Administration.

None of these steps is likely to expand the government’s footprint significantly. But the moves are making the mortgage system more reliant on the federal government — and thus harder to wean from Washington’s help — contrary to the stated wishes of both the administration and Republicans.

“It’s difficult to have any significant pullback without potentially damaging the U.S. economy,” said David Stevens, Obama’s former FHA commissioner and now the president of the Mortgage Bankers Association.

An Obama administration official acknowledged there is a tension between scaling back the government’s role in housing and making sure the current market recovers. The official said the administration continues to believe that in the long run the government ought to have a smaller role, but it is trying to be careful that the steps taken don’t destabilize the fragile housing market.

In the years since the banking system went into crisis after making trillions of dollars of risky mortgage loans, the taxpayer-backed mortgage giants Fannie Mae, Freddie Mac and the FHA funded or insured 90 percent of new loans. That has effectively nationalized the U.S. mortgage business, putting taxpayer money at risk and keeping private-sector money on the sidelines.

Earlier this year, the administration released a white paper, which made clear that it wants to reduce the role of Fannie, Freddie and the FHA over the long term. But officials are trying to strike a difficult balance. They have said that existing housing programs are crucial to making sure people can still buy and sell homes at a time when banks are averse to offering mortgages that don’t carry a government guarantee.

Many Republicans, meanwhile, are skeptical of the government’s role in housing, arguing that an excessive government emphasis on housing in the past two decades fueled the housing bubble and crash. Some have called for a rapid and substantial reduction in the government’s housing role; others favor a more gradual approach.

“It’s very easy to pay lip service to the need to reduce the government footprint in the housing market,” said Guy Cecala, publisher of Inside Mortgage Finance. “But can you do it in a depressed housing market like we’re in now?”

At the center of this debate is the nation’s badly battered mortgage finance system. That’s the system that allows banks to get money to make mortgages by selling them to investors around the world. Since the onset of the financial crisis, banks have only been willing to make loans, and investors have only been willing to invest in them, if they carried government guarantees.

Federal housing agencies have taken baby steps to increase private-market participation in the mortgage market. For example, the maximum loan amount that Fannie and Freddie can back was reduced on Oct. 1 to $625,500 in expensive areas and $417,000 in most areas. FHA continues to insure $729,750 mortgages in expensive areas.

A longer-term debate is whether there should be a federal role in housing whatsoever. Many Republicans don’t think so, but Obama’s top advisers have generally agreed that it makes sense for the federal government to continue playing a substantial role in lending, providing loan insurance in the face of a massive decline in the housing market.

Such a role would likely keep the nation’s housing markets operating as they generally have for the past few decades, with the 30-year fixed-rate mortgage being the norm.