President Barack Obama said Thursday he was sorry that thousands of Americans were losing their health insurance, expressing regret for the first time that the Affordable Care Act hadn't lived up to his promise that people who liked their coverage could keep it.

Mr. Obama said he had intended to make good on his pledge but the administration wasn't as clear as it should have been in describing the changes the new health law would bring. Now, facing a chorus of complaints as many people receive notice that their plans have...