With less than two weeks left to sign up for private health insurance through Maryland’s online marketplace, state officials announced Tuesday that residents who start enrollment by the March 31 deadline — or express interest by calling a hotline — will be allowed to finalize their enrollment later on.

This decision buys the state a little more time to enroll as many people as possible in health insurance plans through the exchange. So far about 40,700 Marylanders have signed up during the enrollment period that ends at the end of this month, far fewer than hoped for when the troubled online site debuted last fall.

Exchange officials say they are optimistic that enrollment will surge in the coming days, citing increased call volume, Web traffic and attendance at enrollment fairs across the state.

At a meeting in Baltimore on Tuesday, the exchange’s governing board also approved spending about $830,000 to extend the contracts of 16 individuals who have been working on the exchange.

That’s an “unanticipated” cost resulting from failures of the system, said Joshua Sharfstein, Maryland’s secretary of health and mental hygiene.