SACRAMENTO, Calif. — California officials said 28,699 people were signed up in the state’s health-insurance exchange in the first week, while New York had more than 40,000 sign up.

The numbers for California, the largest U.S. state by population, were for the Oct. 1-5 period and exceeded expectations, Peter Lee, executive director of Covered California, said at a news conference Tuesday in Sacramento. New York, the third- most-populous state, said in a statement that its pace of sign-ups shows the exchange is “working smoothly.”

In Washington state, the state-run exchange had a rocky start Oct. 1 but managed to quickly turn things around by adjusting certain parameters on its website to alleviate bottlenecks. By Monday, more than 9,400 people had signed up for coverage. The Washington Health Benefit Exchange does not require users to create an account before browsing plans.

“The site is up and running smoothly,” said Michael Marchand, a spokesman for the Washington exchange. “We’re seeing a lot of use, a lot of people coming to the website. If anything, I think it’s increasing.”

Other states reporting a steady stream of enrollments include Connecticut, Kentucky and Rhode Island.

The Oct. 1 rollout of the Affordable Care Act exchanges has faced technical issues, with consumers unable to access parts of the U.S. government’s website that serves people in 36 states. California, one of 14 states running its own website, has fared better. Success is critical in California, where the Obama administration has sent almost $1 billion in exchange grants.

Alan Weil, executive director of the National Academy for State Health Policy, an independent nonpartisan group, credited the relative early success of some state exchanges to the fact that they could leap on problems more quickly than the sprawling, complex federal marketplace.

“Individual state operations are more adaptable,” Weil said. “That does not mean that states get everything right. But they can respond more quickly to solve problems as they arise.’’

In addition, some states allow consumers to shop for insurance, comparing costs and benefits of different policies, without first creating an online account — a barrier for many people trying to use the federal exchange.

The insurance exchanges are a core part of the 2010 law that seeks to provide health coverage for most of the 48 million uninsured Americans. People can select from health plans sold by private insurers and, depending on income, may be eligible to have their premium costs subsidized with federal tax credits. Some also may be eligible for coverage under an expansion of Medicaid, the joint state-federal plan for the poor.

Daniel Mendelson, chief executive of Avalere Health, a research and consulting company, said: “On balance, the state exchanges are doing better than the federal exchange. The federal exchange has, for all practical purposes, been impenetrable. Systems problems are preventing any sort of meaningful engagement.’’

Compiled from Bloomberg News, The New York Times and The Washington Post