AUGUSTA — It could take four weeks for analysts to determine the cost of a computer malfunction that resulted in up to 19,000 people receiving MaineCare services even though they were ineligible, Health and Human Services Commissioner Mary Mayhew said Wednesday.

The error, which was caused by one computer that pays bills not communicating with one that deals with eligibility, was discovered in a computer system that went online in September 2010 and has required “hundreds and hundreds of fixes” since then, Mayhew said. Nineteen-thousand people received at least one service covered by MaineCare, the state’s Medicaid program, between September 2010 and December 2011.

“All of these people would have received a letter saying they were no longer eligible,” Mayhew told reporters in a conference call. But their MaineCare cards remained in effect and they continued to receive services after ignoring, misunderstanding or failing to see those letters, the commissioner said.

The problem comes to light as Republican Gov. Paul LePage tries to cut what the administration says are runaway and unsustainable costs of MaineCare. Mayhew revealed the problem Tuesday to legislative leaders and members of the Appropriations Committee, and on Wednesday explained it to the Health and Human Services Committee.

The problem appears to have occurred because the computer system that deals with eligibility was never designed to communicate with the billing system, resulting in some cases not being properly closed. The problem was discovered in January, and officials are now able to go into the system and close cases retroactively, Mayhew said.

The commissioner said it will take at least four weeks to ascertain the cost of the glitch, “and we want to make sure it’s done comprehensively and accurately.” Mayhew said prospects for recouping money that shouldn’t have been paid for services were not good, noting that MaineCare cards shown to providers indicated the holder was eligible.

“Our focus is really to make improvements in the system,” she said.

Groups that were critical of LePage’s budget, which slashed benefits for thousands of MaineCare recipients, were angry about the computer problem, which they said was revealed to legislators months after being was discovered. The Maine Can Do Better Coalition asked for an investigation.

Democrats said they had questioned MaineCare numbers as they were being reviewed by the Appropriations Committee before the cuts in services.

“We got nothing. In fact, at times, because of our questions, we were accused of being obstructionists,” said Assistant Senate Democratic Leader Justin Alfond of Portland. “And, only now, after a budget has been passed, the administration is coming forward and raising red flags.”

The 19,000 represents 5 percent of the 361,000 Mainers enrolled in MaineCare.