Despite his administration's quiet move overnight to ease the individual mandate for some Americans, President Obama said today the requirement will "absolutely" be enforced starting April 1, 2014, when everyone must have health insurance or pay a fine.

Speaking at an end-of-year news conference, the president insisted that there will be no delay of the mandate as some Republicans have repeatedly called for.

Obama said the decision late Thursday to grant a "hardship exemption" to people who received health plan cancellation notices under the Affordable Care Act was aimed at helping a "very specific population" who "had problems during this transition period."

"What we are constantly doing is looking - is this working the way it's supposed to, and if there are adjustments that can be made to smooth out the transition, we should make them," he said. "But they don't go to the core of the law."

The president said extending the hardship exemption to those facing cancelled plans was "essentially an additional net in case folks might have slipped through the cracks," allowing them the chance to opt for a cheap catastrophic plan as a stopgap to maintain coverage.

"We expect it's going to be a relatively small number because these are folks who want insurance, and the vast majority of them have good options," he said.

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 exemptions was aimed at helping them maintain basic health insurance protections ahead of Monday's sign-up deadline for plans effective Jan. 1.

Obama announced separately that more than 1 million Americans have selected health plans through state and federal marketplaces created by the health care law since Oct. 1. The open enrollment period closes on March 31, 2014.