Obama, with his approval rating tanking and fellow Democrats in open revolt, promised to fix website and coverage failures that have hampered the rollout of the new law and sparked an opening for gleeful Republicans.
The sports-mad president chose an American football metaphor to encapsulate his remorse.
"These are two fumbles on ... a big game, but the game's not over," Obama said, announcing a plan to make good on his discredited promise that Americans who liked their existing health care plans could keep them.
"Everybody is properly focused on us not doing a good job on the rollout." And that's legitimate and I get it.
"There have been times where I thought we were, you know, slapped around a little bit unjustly. This one's deserved, all right? It's on us."
But the president denied that he had known ahead of the website's launch on October 1 that it would not work properly.
"Had I been informed, I wouldn't be going out saying, 'Boy, this is going to be great,'" Obama said, though he warned that buying health care was a complicated business and was "never going to be like buying a song on iTunes."
Obama's apology came as his second term risks being consumed by controversy over the health care law, with Capitol Hill Democrats particularly showing signs of panic that plummeting public confidence in the president could hamper their own prospects in mid-term elections next year.
In a Quinnipiac University poll this week, the president's approval rating plunged to a lowest ever 39 percent and surveys show his previously solid ratings on character and trust eroding.
Republicans, who en masse opposed Obamacare, immediately warned that his contrition did not go far enough.
"President Obama needs to admit that Obamacare cannot be fixed," said Eric Cantor, the Republican House Majority leader.
"Pointing fingers and claiming ignorance is not leadership. For four years, the President told the American people they could keep the plans they liked and costs would go down, and even he now acknowledges that was simply not true."
Mitch McConnell, the top Republican in the Senate, insisted the only remedy was to dismantle the president's proudest domestic achievement.
"What makes this admission even worse is the fact that it was prompted not by the heartbreaking stories of millions of Americans, but by the private pleadings of a handful of endangered Democrats," McConnell said.
"Americans are becoming increasingly aware of the fact Obamacare is broken beyond repair."
The president's current political woes stem partly from his repeated assurance that those with health care plans could keep them when Obamacare comes into force.
But that turned out not to be true as hundreds of thousands of Americans received notices from their health insurance companies that their policies would be cancelled as they did not satisfy the higher quality requirements of the new law.
Obama announced Thursday that policy cancellations would be postponed for a year while Obamacare's problems are fixed.
"The American people -- those who got cancellation notices deserve and have received -- an apology from me," Obama said.
While admitting that the online marketplace for consumers to find new health plans had a "rough start," Obama warned his political opponents not to try to overturn the entire law.
"I will not accept proposals that are just another brazen attempt to undermine or repeal the overall law and drag us back into a broken system," he said.
Figures released Wednesday showed only 106,185 people have been able to register for the program, 1.5 percent of the number the administration had planned to recruit by the end March next year.
Obama's plans did little to placate his foes or allies.
Democratic Senator Jeanne Shaheen called for a two-year transition period.
Republican Senator John Hoeven complained: "Obama's fix is "like closing the barn door after the horse has bolted."
"I just don't think it's going to work, it's not enough. We really need to... get rid of Obamacare and start over."