OLYMPIA, Wash.OLYMPIA, Wash. (Reuters) - Washington Governor Jay Inslee on Tuesday said he was considering mandatory measures to prevent an increase in coronavirus cases that could reach 64,000 in the state within eight weeks unless "real action" was taken.

Inslee said epidemiologists warned there were likely as many as 500 to 2,000 coronavirus cases in Washington, and given the rate of spread of the highly contagious respiratory illness, the number could double every five to eight days.

Washington state cases jumped by 105 to 267 cases on Tuesday with 24 deaths, nearly all of them in the greater-Seattle area.

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"Whether it's 500 today or 1,500 or 2,000, that just goes to a very large number, very quickly," Inslee said.

Asked by reporters whether he was considering mandatory measures like school closures statewide, or just in hard-hit areas, Inslee said he expected to have news on that "in very short order."

"Shutting down any social activity has profound consequences in people's lives," said Inslee. "You have to see if there are ways to reduce them or ameliorate that."

"If there are 1,000 people infected today, in seven to eight weeks there could be 64,000 people infected in the state of Washington if we don't somehow slow down this epidemic," Inslee said. "And in the next week it could be 120,000 and in the next a quarter of a million."

There were reports following Inslee's briefing that he suggested a statewide lockdown was possible.

"He did not say that," Inslee spokeswoman Tara Lee said in response to a question on these reports.

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New York is closing schools, houses of worship and other large gatherings in the suburb at the center of that state's outbreak.

Most schools have stayed open in the Seattle area, drawing criticism as the area reported nearly all coronavirus deaths in the United States.

"New York under the leadership of Governor Cuomo is taking some of the strongest and sensible mitigation steps in U.S.," tweeted Scott Gottlieb, former head of the Food and Drug Administration. "It stands in stark contrast to Washington State, which has been slow to act forcefully in Seattle."

Washington coronavirus deaths have been among nursing home residents, with two more care facilities reporting fatalities on Tuesday.

Nineteen residents of the Life Care Center Kirkland have died, as well as one at an Issaquah home and another at a Seattle senior-living facility, King County reported.

After a delay, testing of Life Care Center staff has begun in earnest, spokesman Tim Killian said on Tuesday. So far, 55 of the nursing home's original 120 residents have tested positive for the virus and 64 of its 180 staff are at home sick with virus symptoms, he said.

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