The total number of customers who selected by Dec. 5 was 1,383,683 plans. They were split nearly evenly between people renewing health coverage, or 52 percent, and the remaining 48 percent being new customers. For the enrollments to take effect, people must pay their first month's premiums.

HealthCare.gov serves 37 states. The data released Wednesday does not include enrollments from the 14 exchanges run by individual states and the District of Columbia.

The number of applications on HealthCare.gov also surged in the third week, growing to 974,018 applications submitted, up from 520,427 the week before.

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The site's telephone call center handled over 982,000 calls, more than double the 484,867 made in the prior week.

"Open enrollment's momentum is building, and I've seen that firsthand as I traveled the country and talked to people, from Florida to New Jersey to Pennsylvania to Texas," said Sylvia Burwell, secretary of the U.S. Health and Human Services Department. "With less than a week left to sign up for coverage that starts Jan. 1, we're encouraging new and returning consumers to visit HealthCare.gov, call the call center, or get in touch with a local assister by Dec. 15."

This Obamacare open enrollment season, the second so far, runs through Feb. 15. Most Americans are required under the Affordable Care Act to have some form of health insurance coverage by that day or be subject to a tax penalty equal to up to 2 percent of their adjusted gross income next year.

Just before open enrollment began, there were about 6.7 million people enrolled in Obamacare plans nationally. Burwell has said she expects there to be about 9.1 million Obamacare enrollees by the end of 2015.

Many of those enrollees are likely to come from current customers. HHS this year is instituting a program that will automatically renew most existing customers in their current health plans unless they select another option.

While that program would support Obamacare enrollment tallies, Burwell and other officials have repeatedly urged existing customers to review their plan options on the government-run exchanges because of the chance they will find a less-expensive option than the one they have, or a plan that better suits their health needs.

Another issue that concerns officials is that a customer's current subsidy that helps them pay for their premiums could be reduced if they accept re-enrollment without shopping for another plan. Those subsidies are tied to the price of certain plans on Obamacare exchanges, and if that benchmark plan changes, it could lead to changes in the value of the subsidies.