With just a month left for Americans to select health plans this year through new insurance marketplaces, the Obama administration is bending some rules to prevent people from being stranded without coverage because of state-run exchanges riddled with computer problems.

In states with dysfunctional insurance marketplaces, the government will for the first time help pay for certain health plans that consumers buy on their own. And once people in those states are able to sign up through the exchanges, their insurance can be made retroactive.

These rewritten rules, laid out in a three-page memo, can be used by any state but are aimed primarily at helping people in Maryland and three other states whose exchanges have not been working well. The four states are among 14 that have each created an insurance marketplace under the 2010 Affordable Care Act.

Some state-run exchanges have had the nation’s greatest successes in attracting people who need insurance, but others have not. The problem-ridden state marketplaces are in Maryland, Oregon, Hawaii and Massachusetts, which pioneered the nation’s first such marketplace but ran into trouble when it suddenly had to interact with a federal computer system to determine people’s eligibility for subsidies.

The other 36 states are relying on the federal online marketplace, HealthCare.gov, which has had its own computer problems, particularly during the first two months after the sign-up period for health plans began in the fall. The states using the federal exchange are not intended to be part of the rewritten rules.

Now, nearly 3.3 million people have enrolled in a health plan between Oct. 1 and Feb. 1.

While affecting only a few states, the changes are significant, in part because they break with what has been a bedrock principle under the 2010 law intended to reshape the nation’s health-care system. Through tax credits to help consumers afford monthly insurance premiums and an annual deductible, the law offers the first federal help the government has given individuals to pay for private health plans. But until now, that help was available only for health plans sold through the new marketplaces — not plans sold outside it.

The rewritten rules were proposed by Oregon Gov. John Kitz­haber (D), who worked them out in a meeting last weekend with Health and Human Services Secretary Kathleen Sebelius, according to a spokeswoman for the governor. “Today’s news means that many more Oregonians will be able to access better coverage at a more affordable cost,” Kitzhaber said in a statement on Friday.

States must decide whether they want to take advantage of the new federal rules, which were announced in the memo issued Thursday and announced Friday by the Centers for Medicare and Medicaid Services, the agency within HHS that oversees the exchanges.

In Maryland, officials are considering several alternatives to deal with its broken marketplace. Dori Henry, a spokeswoman for the Maryland Health Benefit Exchange, said Friday that officials were trying to digest the implications of the federal offer. “We’re pleased that new options are becoming available to help individuals who have experienced problems,” she said.

Early this week, Carolyn A. Quattrocki, the exchange’s acting executive director, told lawmakers that about 7,000 applications are stuck in Maryland’s system, but that does not mean all of those applicants still need health insurance. As of Feb. 22, nearly 36,000 Marylanders had enrolled in a private health plan through the exchange — far below an original goal of at least 150,000 people signing up by March 31, when the first open-enrollment period across the country ends.

Maryland offered retroactive coverage once before to consumers who got stuck in the enrollment process. In January, after the deadline for people to have coverage when it first became available on New Year’s Day, the four carriers participating in the state’s exchange allowed a one-week window during which people could sign up for insurance retroactive to the first of the year. People from about 300 households signed up.

The rewritten federal rules would allow people to receive federal subsidies for health plans outside exchanges as long as the covered benefits are comparable to those of plans sold through the exchanges.

In order to get retroactive subsidies, people will have to start to pay the full price of their health plan, then get the reduction once their state’s exchange is working well enough to determine whether their incomes make them eligible for the help.

Clare Krusing, a spokeswoman for America’s Health Insurance Plans, the industry’s main trade group, said that “this latest change adds to the operational challenges in processing enrollments.” But she added, “Health plans will continue to work with state and federal agencies to help consumers through the enrollment process.”

The rewritten rules are the latest shift to accommodate various constituencies. In November, President Obama bowed to pressure from consumers angry to be losing insurance that did not meet new benefits requirements. The president said that such substandard plans, which were to have been taken off the market in January, could be sold for an additional year.

And this month, administration officials, for the second time in a year, gave medium-size and large employers more time before they must offer health insurance to almost all their full-time workers.