WASHINGTON - Several million people hit with new federal fines for going without health insurance will get a second chance to sign up starting Sunday, and that could ease the sting of rising penalties for being uninsured.

But as the enrollment window reopens, it's unclear how many know about the time-limited opportunity, let alone will take advantage of it.

Fines payable to the IRS are the stick behind the offer of taxpayer-subsidized private insurance under President Obama's health-care law. Virtually everyone in the country is now required to have coverage through an employer or a government program, or by buying individual policies.

This is the first year fines are being collected from uninsured people the government deems able to afford coverage. Tax preparation company H&R Block says the penalty averages about $170 among its affected customers. It usually is deducted from a person's tax refund.

Those penalized are mainly the kinds of people the law was intended to help: low- and middle-income workers who do not have coverage on the job or are self-employed. Roughly four million people are expected to pay fines, according to congressional estimates. Many more will qualify for exemptions.

Travel agent Charles Baxter of Phoenix said his tax refund was reduced by $247 for being uninsured in 2014. He had not heard about the second chance to sign up for 2015 coverage.

Baxter says he will take another look now, but is not sure whether he will opt to buy insurance. Much of his income goes to help take care of his mother, who has health problems.

"I may have to see if any of the health-care costs have changed, to where I might be able to squeeze it in," he said. He said he supports the overall goals of the health law, but says the government should also look at someone's expenses - not just income - before assessing the fine.

Penalties for being uninsured are going up this year, to a minimum of $325 for the full 12 months. That's a significant increase from the $95 minimum in 2014.

The new sign-up opportunity runs through April 30. To qualify, individuals have to certify to the government that they meet certain conditions, including:

They did not know or understand that they were legally required to have coverage until after open enrollment officially ended Feb. 15.

They owed a penalty for being uninsured in 2014.

Those requirements are for the 37 states served by the federal HealthCare.gov website. States running their own insurance exchanges may have different rules and deadlines. Penalties for 2014 are not refundable.

The Obama administration acted after Democratic lawmakers raised concerns. With open enrollment officially over, someone who was uninsured and filed a tax return after Feb. 15 would not have been able to get coverage for 2015. That person would owe the penalty for 2014 and could get locked into a bigger fine for 2015.

The administration is publicizing the special sign-up period as tax filing season continues. For customers who paid a fine, major tax preparation companies are notifying them about the second chance to get coverage.

Tax preparers and some public policy experts have urged the government to move the health care law's sign-up period so it dovetails with tax-filing season. People expecting a refund might be willing to spend some of it on health insurance.