ST. PAUL — Minnesota’s health insurance exchange on Wednesday released its first data on enrollment, showing that two weeks into its launch more than 3,700 people have signed up for health insurance coverage.

It’s a relatively slow start to the state’s delivery system for increasing insurance coverage rates under the federal health overhaul. MNsure officials said 3,769 people have either finalized enrollment or are waiting for payments to be processed, while an additional 1,800 people have completed the application process but not yet chosen an insurer. That’s out of an estimated 300,000 uninsured Minnesotans, and several million more eligible to buy insurance on the exchange.

MNsure’s executive director, April Todd-Malmlov, said she expects the pace of enrollment to pick up speed with the approach of a Dec. 15 deadline to lock down coverage before it takes effect Jan. 1.

“We are happy with the numbers so far and we think most of our enrollment is going to come in December,” Todd-Malmlov said Wednesday, after presenting the initial enrollment snapshot at a meeting of MNsure’s board of directors.

Between those who already signed up and those who just need to pick an insurer, 5,569 people in all have completed the application process. MNsure estimates the number of people who will be covered under those plans at 11,684 — since many plans cover more than one person in a family.

The agency expects slightly less than half of those who have completed the application will receive some kind of tax subsidy or government assistance to help pay for coverage. The agency currently is not compiling information about how many people signing up are among the 300,000 without insurance, but Todd-Malmlov said there are plans to issue surveys at a later date that would give a sense of how well MNsure is reaching the uninsured.

MNsure has set a goal that 823,755 people will obtain insurance through the site by the end of 2014. Under the federal law, people without health insurance coverage face financial penalties beginning in March.

Todd-Malmlov said MNsure has been trying to resolve technical problems that have prevented customers from paying for their plan through the website. She said enrollees will be able to pay for plans in November and December.