MNsure officials said Wednesday that the online marketplace for health insurance has fixed the identity-verification problems that at one point kept half of interested shoppers from creating accounts and pricing health benefits on the site.

MNsure Executive Director April Todd-Malmlov said 96 percent of those trying to create accounts Wednesday were having success and no trouble verifying their identities. Most of those still struggling with the website, she said, were providing inaccurate answers to the system’s personal security questions. Those questions are based on existing public records and query people about items such as the cars they have driven, the cities in which they have lived, and the employers for whom they have worked.

“We have largely passed this point in the road on [problems with] identity proofing,” Todd-Malmlov said.

The early glitches were frustrating to many Minnesotans who were excited by the opportunity to shop for health insurance — especially those who, before the new federal law took effect, had been rejected for coverage because of existing medical problems.

In an e-mail to the Star Tribune on Tuesday, Mary Jean Mulherin likened the site to a “techno vortex from hell.”

“I finally was able to get into the ‘security’ area of MNsure website, and then when I entered a password, strictly following all the rules, it continued to ‘bounce me out’ and I had to start all over again,” she wrote.

Identity verification is just the first step for people seeking to buy health coverage on MNsure, the state online marketplace created under the federal Affordable Care Act as part of the effort to extend health insurance to the state’s 490,000 uninsured residents. Users then create accounts by which the state determines if they are eligible for public programs or subsidies on premium with private-sector carriers. Then they shop among the plans on the site and compare them by premiums and deductibles.

How many Minnesotans have actually used the site already to buy health insurance for 2014 is unclear. MNsure officials won’t disclose a number until Oct. 16.

But they said more than 33,000 visitors have been on the site in its first week, and both individuals and small businesses have created accounts with which to buy coverage.