The federal government on Thursday continued to tackle technological problems that have prevented many Americans from buying insurance on the new marketplaces created by the health-care law.

Health insurers and individuals, meanwhile, have begun reporting limited cases of successful enrollment through the online exchanges.

“Most of day one and two we didn’t see enrollments,” Cigna spokesman Joe Mondy said. “But we’ve been able to start getting enrollments as of last night.”

Mondy confirmed that Cigna has received enrollment in Florida, one of the 34 states where the government is running the marketplaces. Since they opened Tuesday, these online enrollment portals have been plagued by long wait times and error messages that have prevented some people from signing up for the Affordable Care Act’s new insurance options.

The Department of Health and Human Services announced early Thursday that it has added additional computer servers to the exchange to handle higher-than-expected traffic and has more engineers working to speed up the site so it can handle a higher volume.

The agency said these changes have reduced by one-third the number of people waiting to apply on the site. Waiting times to speak to a representative at the call center have been cut in half since the marketplaces began.

“In the last two days, 7 million Americans have visited to learn about their options,” HHS spokeswoman Joanne Peters said by e-mail. “Experts are working around the clock and were able to expand system capacity somewhat overnight, cutting by one-third the volume of people waiting to apply. Work on the site continues today to meet the demand and excitement generated in just the first 48 hours of our open enrollment.”

Cigna, which is selling on five state marketplaces, began receiving enrollments Wednesday night after two days with no sign-ups.

“My understanding is there’s not a heck of a lot of enrollments across the industry, which is reasonable” he said. “Folks are looking at plans. We don’t expect enrollments to go from a trickle to a wave until November. The bottom line for us is that the system is working. It’s very encouraging.”

Chad Henderson, a 21-year-old student in Flintstone, Ga., managed to buy health insurance through the marketplace Tuesday morning. He began shopping around midnight Monday — right when the exchanges opened — and finished about 3 a.m.

“I had to wait like everybody else,” Henderson said. “Millions of people apparently got on the Web site. It took me till about 3 a.m. to create an account. That was probably the longest thing. After creating an account and getting logged in, it was pretty smooth sailing.”