More than 40,000 New Yorkers signed up for insurance on the state’s ObamaCare health exchange in the first week, officials said Tuesday.

That topped enrollment in all other states, the New York Health Department said. Officials estimated that 1 million of the 2.7 million uninsured New Yorkers will get coverage through the state’s insurance marketplace.

“What the 40,000 people represent to me is . . . that there is vast interest in applying for coverage through our state marketplace,” said Donna Frescatore, executive director of the New York State of Health exchange. “It started a little rockier than we’d like,” Health and Human Services Secretary Kathleen Sebelius admitted in an interview on “The Daily Show.”

“And our system is processing applications quickly and efficiently.”

New York and California are the two biggest markets for signing up millions of uninsured Americans under President Obama’s health-care law.

State officials called the data an early indicator of strong demand for new insurance plans that will take effect in 2014.

The disclosures from New York and California come as Republican opponents of Obama’s health-care reform press the administration for details of how enrollment is progressing.

The federal government has been working to tweak issues that have plagued the Healthcare.gov Web site since the exchanges launched Oct. 1.