SEATTLE — The Washington health exchange, which signed up another 20,000 people for private health insurance over the weekend, announced Monday it would be giving people two more months to enroll.

The exchange said 160,000 signed up for private insurance during the open enrollment period that ended Sunday night, including 66,000 new customers and about 94,000 people who renewed insurance they bought during the previous open enrollment period.

The exchange is still more than 50,000 away from its enrollment goal of 213,000 for this year.

The special enrollment period that ends April 17 will basically be for anyone who hasn’t bought health insurance for 2015, since one of the ways people can qualify for the extension is by saying they didn’t realize how big the tax penalty would be if they don’t have health insurance.

When people file their taxes in early 2016, those who didn’t have health insurance in 2015 will have to pay a penalty of $325 per adult and $162.50 per child in their household. The family maximum penalty is $975 or 2 percent of income, whichever is greater.

Although the cost of insurance may still be higher than the cost of the penalty, the two amounts will get closer during the second year of tax penalties.

The penalty for those filing returns this year is $95 per adult, $47.50 per child, but not more than $285 per family or 1 percent of the family income, whichever is greater.

Richard Onizuka, CEO for the Washington Health Benefit Exchange, acknowledges that the deadline extension will likely help the exchange get closer to its enrollment goal, but he insists that isn’t the point.

“We just want to make sure the consumers had one more chance,” Onizuka said. “The main thing is to give the consumers as many options as we can.”

The exchange, its community partners and health insurance companies will all be working to reach out to people who haven’t renewed their insurance and to those who started an application this year but didn’t finish it.

Onizuka said they’ve been bombarding people with phone calls, emails and advertisements.

“Foremost for us is to try to make sure consumers have what they need and have good health insurance,” he said.