CHICAGO — Anticipating heavy traffic on the government’s health care website, the Obama administration extended Monday’s deadline for signing up for insurance by a day, giving Americans in 36 states more time to select a plan.

It was the latest in a series of pushed-back deadlines and delays that have marked the rollout of the health care law.

But federal officials urged buyers not to procrastinate.

“You should not wait until tomorrow. If you are aiming to get coverage Jan. 1, you should try to sign up today,” said Julie Bataille, a spokeswoman for the federal agency in charge of the overhaul.

Bataille said the grace period — which runs through Tuesday — was being offered to accommodate people from different time zones and to allow for any technical problems that might result from a last-minute rush of applicants.

The HealthCare.gov site had a disastrous, glitch-prone debut in October but has gone through extensive improvements to make it more reliable and increase its capacity, and the administration said the system was running well Monday.

By the afternoon, the site had received a record 850,000 visits, five times the number logged by the same time last Monday, the administration said. Bataille said the system was handling the volume with error rates of less than 1 in 200 and response times of less than one second.

The Obama administration is hoping for a surge of year-end enrollments to show that the technical problems were merely a temporary setback. That would also go a long way toward easing concerns that insurance companies won’t be able to sign up enough young, healthy people to keep prices low for everyone.

The administration was careful not to characterize Tuesday as a new deadline or an extension, likening the move instead to the Election Day practice in which people who are in line when the polls close are still allowed to vote.

Monday had been the deadline for Americans in the 36 states served by the federal site to sign up if they wanted coverage at the start of the new year. The remaining states operate their own online marketplaces, and some of them have also extended their deadlines.

As the deadline drew new, more than 1 million people visited the website over the weekend, and a federal call center received more than 200,000 calls.

Roger Colyn, 60, of Des Moines, Iowa, was happy when he left his Monday morning appointment with a state enrollment navigator. She helped him sign up for a “silver” plan that will cost him $10.79 in monthly premiums after government aid is factored in.

“I feel relieved,” Colyn said.