Maryland Gov. Martin O'Malley speaks at a news conference in Baltimore on Dec. 13, 2013. O’Malley said Friday he plans to introduce emergency health legislation tied to the state’s new exchange program. (Patrick Semansky/Associated Press)

Maryland lawmakers are expected to pass legislation as soon as next week to assist the hundreds of people — or, possibly, thousands — who tried to sign up for health insurance through the state’s new exchange program, encountered problems and were left uncovered when the new year began.

Gov. Martin O’Malley (D) and Lt. Gov. Anthony G. Brown (D) said Friday that they plan to introduce emergency legislation that would expand enrollment in the Maryland Health Insurance Plan, a separate state-run program that normally covers high-risk individuals. Those enrolled would have to pay a premium, which is determined by income but is often slightly higher than market rates, and would probably be allowed to stay on the plan for only a few months.

State officials said they did not know how many people were unable to sign up on the exchange’s Web site, Maryland Health Connection, but estimated that it could be anywhere from a few hundred to as many as 5,000.

Brown, who was put in charge of implementing the Affordable Care Act in Maryland, repeatedly described these people as being stuck without insurance “through no fault of their own.” Officials said this short-term fix could cost the state $5 million to $10 million, depending on how many people enroll and how much medical care they need.

O’Malley also offered his most detailed comments to date on whether ongoing technological problems with the exchange’s Web site might force the state to turn over part of its online enrollment to the federal health-care Web site or partner with other better-functioning states.

The governor and Brown had previously bristled at the idea, but O’Malley said Friday that “we may very well reach a point where we do that on a temporary basis, [or] we do it for a portion of those who come on to our site,” to give state IT experts breathing room to fix the state exchange.

O’Malley said it is difficult to discern how many people tried to get insurance and were unsuccessful. Some residents thought they had completed the process, he said, and were then surprised when an insurance card never arrived.

Maryland officials have yet to formulate standards on who would qualify for the state-subsidized coverage, which would be retroactive to Jan. 1, and what proof they would have to provide for having tried to use the exchange system.

State officials were among the earliest and most enthusiastic supporters of President Obama’s Affordable Care Act, and Maryland was one of 14 states that opted to build and run its own health-insurance marketplace. The O’Malley administration had promised repeatedly to provide one of the best Web sites in the country. But Maryland’s site has been plagued with technological problems since its debut on Oct. 1. The site crashed on the first day. Since then, residents have encountered a variety of error messages, frozen accounts and incorrect information, and the system has failed to transmit key enrollment data to insurers.

State officials say they have made a series of improvements to the site and will continue to perfect it — but the emergency legislation is yet another reminder of the problems.

For comparison, federal officials announced this week that 2.1 million people had signed up for insurance through and that of those, 7,000 had reported problems with the Web site to a hotline and were being considered for retroactive coverage.

Maryland announced Friday that 61,322 people had enrolled through the exchange, although the bulk of those were through Medicaid. Perhaps as many as 5,000 remained mired in the Web site. That number is “an estimate, it may be more; it may be less,” said Maryland Health Benefit Exchange spokeswoman Dori Henry.

Timothy Stoltzfus Jost, a health-care expert and professor at Washington and Lee University School of Law in Lexington, Va., said Maryland’s numbers suggest that the state’s problems may be worse than some estimated.

“Maryland has had problems, but the numbers sound much worse than the federal exchange. . . . It is really a problem when people have been trying to sign up and cannot. I’m glad they’re trying to help those people,” he said.

Joshua Sharfstein, O’Malley’s health secretary and chairman of the board of the quasi-public Maryland Health Benefit Exchange, acknowledged that the state would have to develop a process to guard against fraud by those seeking the retroactive insurance.

Sharfstein said those seeking coverage might have to sign a “legal affidavit” attesting to their failed efforts to sign up for insurance online in order for the state to agree to help pay for medical costs already incurred. Those details would probably not be included in the emergency legislation that would be introduced when the legislative session begins Wednesday, but they would be addressed soon after, he said.

The Maryland Health Insurance Plan was created in 2002 to assist people with preexisiting conditions who had difficulty getting insurance. Now with the Affordable Care Act, which provides protection for patients with preexisting conditions, Maryland is in the process of phasing its program out.

The program is largely funded by a tax paid by hospitals and has at least $40 million on hand, according to state officials. The millions of dollars that the emergency legislation is expected to cost will come from that fund.

By the end of March, Maryland aims to have at least 150,000 residents enrolled in private plans. As of late December, that number was at just more than 18,000.

O’Malley suggested that the state would not hit the 150,000 target, saying that “maybe double” the number enrolled so far would sign up by the March deadline, when people can be fined under the federal law for not carrying insurance.

At the same time, the governor said enrollment in Medicaid has exceeded expectations. The state has already signed up 130,000 new Medicaid-eligible enrollees, including more than 41,000 who signed up through the Web site. The original estimate was 110,000 for the first month.

But the disclosure that just 18,000 had signed up for private plans drew criticism from Republicans and one prominent state Democrat, who has called for Maryland to abandon its troubled Web site in favor of the federal site.

“Total private coverage enrollment of 18,257 Marylanders is only 12 percent of the private enrollment goal of 150,000 Marylanders, meaning the national level is outperforming Maryland,” Rep. John K. Delaney (D-Md.) said in a statement. “These numbers indicate that while clear improvement is occurring at the Maryland Health Exchange, we are still lagging behind the national numbers, and we need to drive further improvement to benefit all Marylanders.”

Lena H. Sun contributed to this report.