Jonathan Ernst / Reuters President Barack Obama delivers remarks on the Affordable Care Act, commonly known as Obamacare, at an Organizing for Action grassroots supporter event in Washington, November 4, 2013.

Significantly more Americans purchased health insurance through new exchange websites in the second month of the new health care reform law than did during the first, according to a report Wednesday, an encouraging sign as the Obama administration seeks to recover from the botched rollout of its signature initiative.

Between Nov. 3 and Nov. 30, 258,497 Americans signed up for private health insurance through the health care reform law’s new exchanges, compared to 106,185 who signed up between Oct. 1 and Nov. 2, according to the report from the Department of Health and Human Services released Wednesday. An additional 803,077 people seeking coverage through the exchanges were found eligible for Medicaid or the Children’s Health Insurance program in October and November, the administration said.

Secretary of Health and Human Services Katheleen Sebelius, who asked her department’s inspector general on Wednesday to investigate the troubled launch of the site, is set to appear before a House health care subcommittee again on Wednesday.

While it appears that the pace of enrollment is speeding up, those seeking private insurance through the exchanges have less than two weeks to select plans to get coverage that begins on Jan. 1. Consumers must select plans by Dec. 23 for coverage beginning then.

The figures released on Wednesday do not reflect the full impact of what federal officials say is a vastly improved HealthCare.gov, the federal web site managing enrollment for 36 states. The site launched on Oct. 1 and was quickly hobbled by major computer problems. On Dec. 1, the administration announced it had made more than 400 software fixes that had enabled HealthCare.gov to operate well for what it characterized as “the vast majority of users.” Federal officials say HealthCare.gov can now accommodate 800,000 users per day.

Asked on a Tuesday conference call with reporters to provide a guarantee that all Americans seeking coverage through the exchanges will be able to do so by Dec. 23, a spokeswoman for the Centers for Medicare and Medicaid Services (CMS) declined to do so. She also declined to provide enrollment figures for the first week of December, when the federal government said HealthCare.gov was operating well. The spokeswoman, Julie Bataille, said CMS is “actively working” with insurance companies to resolve a worrisome problem with HealthCare.gov — that it has been transmitting correct consumer data to insurers. Bataille had previously said that the rate of electronic errors on HealthCare.gov applications sent to insurers had decreased from 25 to 10 percent. Consumer advocates and insurers have warned that these errors could lead some consumers to believe they have coverage when they do not. Bataille has said consumers should contact insurance companies directly to verify their enrollment through HealthCare.gov.

“We invite Americans whose experiences with HealthCare.gov have been frustrating to come back and try again,” Michael Hash, director of the HHS’s Office of Health Reform, told reporters. Despite the early slow pace of enrollment, Hash said HHS still believes it will meet a previous estimate that some 7 million Americans will sign up for private health insurance through the exchange by March 31 when an open enrollment period ends. “We think we’re on track and we will reach the total,” he said.

As in October, enrollment through exchanges being run by states outpaced sign ups through HealthCare.gov in November. As of Nov. 30, 137,204 people had signed up for coverage through the federal exchange, compared to 227,478 who signed up on state exchanges. Nearly half the state total occurred through California’s exchange.

The figures in Wednesday’s report include those who have selected private health insurance plans, even if they have no yet paid their first month’s premium, which is required for coverage to begin on Jan. 1.