WASHINGTON — President Obama urged Americans who have flocked to the new government-run Web marketplaces for health insurance policies not to give up because of the technical problems attributed to greater-than-anticipated demand. Fixes are under way, he said.

Mr. Obama, in an interview with The Associated Press released on Saturday, said he did not have any figures to counter scattered reports that just a very small number of people have succeeded in signing up for insurance coverage since state and federal Web sites began enrollment on Tuesday for the so-called insurance exchanges. Those are a central part of Mr. Obama’s health care law, which was passed in 2010 to extend coverage to those who do not get insurance benefits on the job.

People “definitely shouldn’t give up,” Mr. Obama said. Citing the slow start to a similar program for Massachusetts residents several years ago, the president predicted that when the six-month window for enrollment ends in March, “we are going to probably exceed what anybody expected in terms of the amount of interest that people had.”

House Republicans — who forced a shutdown of the federal government, which also started on Tuesday, by demanding that the health care law be defunded or delayed as a condition for their approving financing for the government in the new fiscal year — were quick to jump on the snags as validation of their opposition to the program.