Empire BlueCross BlueShield has agreed to give three weeks of free coverage to those consumers who signed up for health insurance on the New York State exchange that began in January but didn't get care in that time because of enrollment problems.

The agreement to be announced on Sunday between the insurer and Gov. Andrew M. Cuomo's administration also requires Empire to pay $2 million for consumer education to encourage enrollment on the exchange, created under the federal Affordable Care Act.

"Empire did the right thing by working to address these issues and delivering relief to consumers," Cuomo said in a statement.

The agreement should impact about 15,000 to 20,000 policyholders, who will receive checks from Empire for the equivalent of three weeks of premiums paid, administration officials said.

Empire, which enrolled the highest percentage of customers on New York's exchange -- 21 percent -- has been plagued with problems since the Jan. 1 start date.

People have complained they didn't receive ID cards; were given the wrong ID numbers; were assigned primary care physicians for which they didn't sign up; were told to send in payments for coverage without having been properly billed or knowing whether they actually had coverage; learned their premium payments have been lost; or discovered that their doctors don't actually belong to the plan. Many said they spent fruitless hours on the phone trying to get some answers.

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Empire spokeswoman Sally Kweskin acknowledged in a statement that "the rollout of the exchange has been turbulent, and some members have been unable to access benefits or get through to our customer service call centers."

That is why, she said, "we will be giving a financial accommodation to those new Empire exchange enrollees who did not receive any care during this first month."

"In the meantime, we will continue to work vigorously to address the issues our members may have experienced," she said.

Empire has also been required to submit a corrective action plan to the state Department of Financial Services, which oversees insurance companies, and make a daily report on their progress, administration officials said.

Some Empire customers were not satisfied.

"It's not enough," said Beth Drucker, 59, of Centerport, whose premium payment was lost and who received ID cards with the wrong primary care physician and ID number. "I logged in 60 hours on the phone. I lost count of how many reps I have spoken to and every rep tells you something different."

Dolores Persky, 51, of Wantagh, agreed. Persky, who has breast cancer that has spread to her lungs, had to fight to keep her oncologist, who was listed on the Empire plan but then turned out not to be.

"I think Empire is just trying to save face right now," she said. "Sending me a check for three weeks is not going to help all the aggravation I went through."

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Anyone with an insurance problem can call the Department of Financial Services hotline at 212-480-6400 or 800-342-3736.