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WASHINGTON – Roughly 40,000 Americans have signed up for private insurance through the flawed federal online insurance marketplace since it opened six weeks ago, according to two people with access to the figures.

That amount is a tiny fraction of the total projected enrollment for the 36 states where the federal government is running the online health-care exchange, indicating the slow start to the president’s initiative.

In comparison, 14 states, including New York, and the District of Columbia are operating separate exchanges, and an analysis released Monday by Avalere Health, a consulting firm that has been tracking sign-ups, shows that about 49,000 people have signed up for coverage in those exchanges – representing about 3 percent of the eventual expected enrollment in those states.

Although the state exchanges have varied in how easy they are to use, few have been marred by technical problems as severe as the federal HealthCare.gov.

The first concrete evidence of the popularity – and accessibility – of the new federal insurance exchange emerged as the White House has been preparing to release this week the first official tally of how many people have chosen coverage using the website, HealthCare.gov.

One administration official said Monday that the official figure will include people who have paid for a health plan and those who simply picked a plan and put it in their online shopping cart.

The administration’s only known previous projections come from internal memos, released on Capitol Hill, that predicted that about a half-million Americans would have selected insurance by the end of October. It was unclear whether that figure, cited in a letter last month by House Ways and Means Committee Chairman Dave Camp, R-Wis., included only people who enrolled in private health plans or also low-income people who joined Medicaid.

In recent days, officials inside the White House and at the Department of Health and Human Services have been working to dampen public expectations for enrollment, in light of a rollout of the online marketplace that they have acknowledged has been disastrous. HealthCare.gov has been riddled with hardware and software problems that have stymied many Americans trying to shop for or purchase a health plan.

“I can tell you our early enrollment numbers are going to be very low,” HHS Secretary Kathleen Sebelius testified last week before a Senate committee.