ST. PAUL — More than 3,700 Minnesotans have signed up for health insurance coverage so far through the state’s new online exchange, according to a report released Wednesday with the first data on enrollment.

The board of directors for MNsure got its first report on the enrollment on Wednesday, two weeks into its launch as the state’s delivery system for increasing health insurance coverage rates under the federal overhaul. MNsure officials said 3,769 people have either finalized enrollment or are waiting for payments to be processed.

Beyond that group, an additional 1,800 people have completed the application process but not yet chosen an insurer. That means that 5,569 people in all have completed the application process. MNsure officials estimated the number of people who will be covered once those plans come into effect is 11,684 since some of the plans will cover families.

Of those 11,684 people so far headed for coverage under MNsure, the agency reported that just under half are likely to get some kind of tax subsidy or government assistance to help pay for their coverage. However, the agency is not currently compiling information about how many people getting coverage through the new venture were previously uninsured.

State officials estimate that eventually MNsure would extend coverage to about 300,000 Minnesotans who didn’t previously have it.

MNsure’s executive director, April Todd-Malmlov, said the agency has experienced some technical problems with letting customers pay for their plan through the website. She said enrollees would be able to pay for plans in November and December. Coverage purchased on the exchange will kick in on Jan. 1.

Todd-Malmlov also said after early delays for some who tried to access the site, that MNsure has upped its success rate to above 95 percent.

In all, just over 12,000 people have opened MNsure accounts along with 355 small businesses. The website, MNsure.org, has had more than 34,442 unique visitors since it launched on Oct. 1. Coverage purchased on the exchange will kick in on Jan. 1, with penalties beginning in March for people who don’t have health insurance after that.

Enrollment data under the federal health-care changes has been hard to come by in the opening weeks. Details about enrollment in the 36 states with exchanges being operated by the federal government won’t be available until sometime in November. Data has been available only in some of the 14 states including Minnesota that are operating their own exchanges.

Another state running its exchange, Kentucky, had reported more than 18,000 people had enrolled by the end of last week. But other states weren’t nearly that far along. Oregon has yet to even open its exchange because of rampant technical problems.

Mitch Grussing, a self-employed musician from St. Paul, told the MNsure board on Wednesday that he had successfully signed up for coverage through the site. There were a few technical glitches, he said, and he was still waiting for the ability to make his initial payment. But Grussing said he would save about $35 a month on his premium from his previous insurance, that his deductible would be cut in half and that he’d be eligible for more office visits.

“I would say MNsure has done its job, at least for me,” Grussing said. “I got exactly what I wanted to get out of it.”