Facing continued fallout over the cancellation of millions of health plans under the Affordable Care Act, the Obama administration is loosening the terms of the individual mandate for some consumers while providing them new options to maintain coverage.

Americans whose individual insurance policies were canceled - at least 4 million people - are now eligible for a "hardship exemption" from the requirement to have insurance, which starts in 2014, the administration said on Thursday.

The designation of a canceled plan as a qualifying hardship means those who have not yet found a suitable replacement have a new option: enroll in a cheap, bare bones catastrophic plan that is typically restricted to people under 30 years-old or others with an exemption.

The Department of Health and Human Services has also launched a new hotline for those who got cancellations to help them through the process.

Close to 500,000 Americans whose plans did not comply with Obamacare and were cancelled for 2014 still have not found suitable coverage, the administration estimated on Thursday. The move to make that group eligible for "hardship exemptions" is aimed at helping them maintain basic health insurance protections ahead of Monday's sign-up deadline.

Health insurers criticized the development, which they said could mean fewer enrollees than they projected when rates were set for 2014.

"This latest rule change could cause significant instability in the marketplace and lead to further confusion and disruption for consumers," said Karen Ignani, president and CEO of America's Health Insurance Plans, in a statement.

The White House disputed AHIP's characterization, citing the experience in Massachusetts, where residents had the option of applying for a hardship exemption from the state's mandate, but very few did.

"This is a common sense clarification of the law. For the limited number of consumers whose plans have been cancelled and are seeking coverage, this is one more option," said HHS spokeswoman Joanne Peters.

The change in policy for those with cancelled plans came in response to a letter by six senators (five Democrats and one Independent) to HHS Secretary Kathleen Sebelius on Wednesday asking her to provide relief for "many of our constituents who are upset."

Sebelius said in a written response to the group last night that the agency would take new steps to accommodate those "not able to renew their existing plans and are having difficulty finding an acceptable replacement in the Marketplace."

Guidance posted by the Centers for Medicaid and Medicare Services said consumers seeking the exemption or enrollment in stopgap catastrophic coverage would need to submit a form and proof of their plan's cancellation to qualify.

Anyone seeking Obamacare coverage effective Jan. 1 must sign-up by 11:59 pm local time on Dec. 23. HHS says more than 365,000 have successfully selected a plan through the state or federal exchanges through Nov. 30. Many states have been reporting a significant surge in sign-ups in December.

The administration had previously delayed enforcement of the individual mandate by three months, with tax penalties for those without coverage set to kick in after March 31. But persistent technical problems with the federal insurance website HealthCare.gov have thwarted sign-ups from those who want their coverage to start at the beginning of the year.

President Obama, who has been criticized for failing to keep his promise that if you liked your health plan you could keep it under Obamacare, acted in November to allow insurers to reinstate cancelled plans for 2014 if they wanted to. But only about half the states accepted the policy, forcing many affected to look for new coverage.

This post has been updated.