Federal Reserve officials are considering new strategies to try to lower mortgage rates and help Americans reduce the burden of debt that hangs over the economy. The major question they face: Would the tools they have at their disposal actually work?

In the past few months, leaders at the central bank have become increasingly convinced that problems in the system of housing finance are preventing the interest rate policies the Fed controls from having their usual economic impact. For example, even after Fed action that helped lower mortgage rates, surprisingly few people were able to take advantage by refinancing because they owed more than their homes are worth.

But with new efforts by federal housing regulators underway to make it easier for homeowners and the Fed running out of other tools, the idea of further intervention in the mortgage markets is gaining new attention at the central bank.

“Clearly we’ve indicated our interest in supporting the mortgage market,” New York Fed President William C. Dudley said following a speech Monday, according to wire reports. “Depending on how the world evolves, we potentially could move to do more in that direction.”

Fed leaders will likely discuss specific options at a policy meeting next Tuesday and Wednesday, though they appear unlikely to take any major actions then. Data in recent weeks have pointed to a slightly improved economy, and many officials are skeptical that any new measures from the Fed to try to lower mortgage or other interest rates would really provide a boost. Three dissented from a related move at a September policy meeting.

“They’re very concerned about what’s going on in the mortgage market, and they’re seriously considering what they can do to help,” said Diane Swonk, chief economist at Mesirow Financial. “But it’s more likely to happen in December or January than now.”

A growing chorus of Fed officials appears inclined to try to support the ailing housing market by buying the mortgage-backed securities issued by Fannie Mae and Freddie Mac. The move would be expected to lower mortgage rates and could have other effects, such as leading private investors to shift money into the stock market and corporate bonds, strengthening financial markets broadly.

“I believe we should move back up toward the top of the list of options the large-scale purchase of additional mortgage-backed securities,” Fed Governor Daniel Tarullo said in a speech last week.

The logic behind such a move is simple: The economy is being held back by consumers who racked up too much debt, particularly home mortgages, in the years leading up to 2007. If the Fed could make those debts more manageable by lowering rates, the economy would be able to heal faster.

Such a policy would work in concert with a new effort by the Federal Housing Finance Agency, announced Monday, to remove some of the obstructions that are keeping large numbers of homeowners from refinancing. The idea is that the combination of low rates and more people able to refinance could leave more money in Americans’ pockets.

A working paper by researchers at the Congressional Budget Office found that such a wide-scale refinancing program could save American households $7.4 billion a year that would then be available for other spending, and result in 111,000 fewer families facing foreclosure. Joseph Gagnon, a former Fed economist who is now a senior fellow at the Peterson Institute for International Economics, argues in a paper that such a policy, coupled with aggressive action to lower mortgage rates by the Fed, could lead to as many as 4 million new jobs.

But those rosy estimates notwithstanding, there are no guarantees that the policy would help much.

For one thing, mortgage rates are already exceptionally low — 4.11 percent for a 30-year fixed-rate mortgage last week, according to Freddie Mac. So whatever the success or failure of the new efforts to ease refinancing, it’s not clear that getting those rates marginally lower would have a major impact on economic growth.

Moreover, when people refinance a higher interest rate mortgage into one with a lower rate, it means that the owner of the earlier mortgage bond gets paid off, and thus would no longer be receiving the higher interest payment. Every dollar that the homeowner saves in lower interest costs means one dollar less income for the lender.

However, many of those lenders are owners of mortgage-backed bonds who are less likely to circulate that money back through the U.S. economy. Central banks, particularly in Asia, hold large volumes of the securities, and the Fed itself owns $867 billion worth. The overall U.S. economy might be healthier if American households had the extra dollars in their pockets from refinanced mortgages than if those institutions kept their above-market interest payments, economists said.

Another argument against the strategy would be that the Fed, by investing in mortgage securities, would be engaging in “capital allocation,” essentially favoring the housing sector over other forms of borrowing such as the corporate sector. The Fed bought $1.2 trillion in mortgage-related securities in 2009 and early 2010, but subsequently shifted toward holding longer-term Treasury bonds instead to address specifically that concern.

Still, with the unemployment rate over 9 percent and the economy growing too slowly so far this year to push that rate down, Fed officials are increasingly looking for whatever tools they can find to try to improve the situation.

“Is this the magic bullet that will fix the economy?” said Tim Duy, an economist at the University of Oregon. “Probably not. But it can be done, and will probably have a positive impact.”