Health insurers and individuals began reporting a trickle of enrollments in the new online marketplaces created by the health-care law, as federal and state officials scrambled to try to fix technical problems that have prevented many consumers from buying coverage.

The White House has declined to release any national statistics on sign-ups, saying complete information was not yet available.

“We don’t have that data,” White House press secretary Jay Carney told reporters Thursday.

Several insurers said that they are recciving at least sporadic enrollment reports from the Department of Health and Human Services, which is running the insurance marketplace for 34 states that have declined to set up their own exchanges.

The department said early Thursday that it added computer servers to the federally run marketplace to handle higher-than-expected traffic and assigned additional engineers 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 for insurance on the federal site, Waiting times for people wanting to speak to a representative at the government’s call center have been cut in half since the marketplaces began operating Tuesday.

“In the last two days, 7 million Americans have visited to learn about their options,” HHS spokeswoman Joanne Peters said in an 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 plans on five state marketplaces, began getting enrollments Wednesday night.

“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 enrollments in Florida, one of the states where the federal government is running the marketplaces. Since the online portals opened, they 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.

Other insurers reported similar results Thursday. Many hesitated to offer specifics, however, because they had yet to verify the information they were receiving from the federal government.

“It’s definitely working,” said Mario Molina, chief executive of Molina Healthcare., which is offering plans in nine states, including several on the exchange being run by the federal government. “I know people have been having difficulty accessing Web sites, but I am told by staff that they were able to get into every state Web site. It’s working.”

After two days without any word on sign-ups, Blue Cross Blue Shield of Louisiana received some reassuring news Wednesday night: Seven people had signed up for its plan on the marketplace that day.

“The first day and second we received no submissions,” spokesman John Maginnis said. “This being day three, we were notified through the website that we had seven. So that’s very good news. It’s a small number, but it told us the functionality is beginning to perform as its supposed to.”

Maginnis said that insurance applications were beginning to pile up on brokers’ desks across the state, as they waited for the online marketplaces to get up to speed before submitting the documents electronically.

“We have been accumulating a lot of paper,” he said. “They’ll be submitting those electronically. They’re being held in queue right now.”

States have attempted to address their most urgent technology problems. In Maryland, officials said the state’s health insurance exchange was showing improvement, and that bottlenecks in creating accounts, the first step in buying a health plan online, were easing. Technicians made some initial fixes to the system Wednesday night, and more than 1,000 new accounts had been created by early Thursday, according to Josh Sharfstein, Maryland’s health secretary.

Some problems persisted. Maryland said Thursday that, because of overnight maintenance, only general information will be available online from 11 p.m. to 5 a.m. daily for the rest of the month. Consumers will not be able to create accounts or shop for plans during that time.

Washington state and California have also taken their sites down for maintenance in the overnight hours, and Washington officials said they would continue to do so as needed.

As a result of the Web site issues, one Maryland insurer, Evergreen Health, pushed back its appointments with potential enrollees until next week. Peter Beilenson, Evergreen’s chief executive, said the co-op had made appointments with 100 people who wanted to sign up for coverage on Friday. “We called them all today and and we’re going to delay that until the following week,” he said.

Elsewhere, shoppers still report difficulties signing up for coverage. Michael Hoffman, a 31-year-old attorney in Florida, estimates that he has attempted to shop on the marketplace about seven or eight times since Tuesday.

Each time, he has run into different error messages and given up on the process.

“I was pretty frustrated,” Hoffman said. “It’s disappointing when you have higher expectations.”

Hoffman now plans to stop shopping until next month, when he expects the site to work better. Coverage purchased on the marketplace does not start until January 1, so he sees little drawback to waiting.

“There’s not much urgency to it,” he said. “The novelty has worn off in trying to sign up.”