Updated

Washington state on Monday became the first state to extend the sign-up deadline for health insurance until mid-April, allowing uninsured people to get health plans while filing their tax returns.

Other states and the federal government’s HealthCare.gov insurance exchange, which serves 37 states, said they, too, are considering extending through the tax season the sign-up period that officially ended Sunday night.

Washington state’s move followed short-term extensions of a few days to a week by a number of state insurance exchanges as well as HealthCare.gov, for reasons including harsh winter weather in some regions and a technical glitch that sidelined some consumers on Saturday. Some states said they would allow consumers who hadn’t completed applications by Sunday to finish them but didn’t stipulate a cutoff date.

Washington state said it extended its deadline until April 17 for residents who hadn’t realized they would face tax penalties under the Affordable Care Act for going without insurance in 2014 and 2015.

“This is the first year that residents may incur a tax penalty for not having health insurance under the Affordable Care Act,” said Richard Onizuka, chief executive officer of Washington’s exchange. “This special enrollment window will allow these individuals—as well as those who experienced difficulty completing their applications—additional time to get enrolled for 2015 coverage.”

The second enrollment period went relatively smoothly for both the state exchanges and HealthCare.gov. But late bumps for the HealthCare.gov site on Saturday, coupled with a jump in last-minute shoppers, prompted federal officials and a number of state officials to say that people could get up to an extra week to finish their applications for health plans for 2015.

Click for more from The Wall Street Journal.