New Yorkers now have until Saturday to enroll through the state’s insurance exchange for health coverage that starts Jan. 1, the state’s health insurance exchange announced Tuesday.

Officials with the NY State of Health said they were extending the deadline for Jan. 1 coverage to accommodate the high volume of enrollees.

“This deadline extension will give New Yorkers the extra time they need to select an affordable coverage plan that’s right for them,” said Donna Frescatore, executive director of NY State of Health, in a statement.

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People have until Jan. 31 to sign up for 2016 coverage. The deadline extension is for individual and family coverage and doesn’t apply to the small business marketplace.

The state said the exchange’s customer service center answered more than 170,000 calls last week, with an average of more than 34,000 a day. Between Nov. 1 and Dec. 10, the exchange’s website has had more than 43 million page views and 1.8 million anonymous shopping searches, state officials said.

Locally, enrollment activity is up too, said Janine Logan, spokeswoman for the Nassau-Suffolk Hospital Council, an official “navigator” agency that offers daily first-come, first-serve enrollment assistance at various Long Island sites.

For the first 11 days of December, she said enrollment with the council had exceeded what is usually seen in the first 11 days of a typical month.

“We’ve been quite busy so the extension for four days is good for anyone who is scrambling to get coverage,” she said.

Jack Glanzer, president of The Granite Insurance Brokerage in Lynbrook, said the state should have extended the deadline earlier. He said he is still dealing with clients who had Health Republic insurance, which the state canceled at the end of November for financial reasons — forcing thousands to scramble for coverage for December.

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“It’s busy anyway this time of year but it’s quadruple the normal volume because of Health Republic,” he said.

Pam Hassen, chief marketing officer at Fidelis Care, said the company has also been busy and the extension is helpful. She said Fidelis has picked up several thousand former Health Republic customers. To ensure that no one was without coverage, the state reached an agreement with Fidelis and several other insurers to automatically enroll Health Republic individuals and families who hadn’t signed up with another company for December.

Hassen said the company offers multiple ways for people to find out what health plans are available at fideliscare.org or at 888-343-3547. To find Nassau-Suffolk Hospital Council navigators, go to: coverage4healthcare.org/insurance_under_65/.

For more information on how to enroll, visit nystateofhealth.ny.gov or call 855-355-5777.