(Adds latest cases, deaths reported in Washington state)

By Andrew Hay and Deborah Bloom

SEATTLE, March 9 (Reuters) - The Seattle-area nursing home at the epicenter of one of the biggest coronavirus outbreaks in the United States said on Monday it had no kits to test 65 employees showing symptoms of the respiratory illness that has killed at least 13 patients at the long-term care center.

The staff in question, representing more than a third of the Life Care Center's 180 employees, are out sick with symptoms consistent with coronavirus, and a federal strike team of nurses and doctors is helping to care for 53 patients remaining in the center.

With the facility in the Seattle suburb of Kirkland accounting for more than half of the known U.S. coronavirus deaths, and all its patients tested, it was unclear why Life Care lacked diagnostic kits for staff, even as the University of Washington offered to process test samples for them.

"We would like more kits to test employees," Life Care Center spokesman Tim Killian told reporters, adding he did not know why they had not been forthcoming.

"We've been asking the various government agencies that have been supplying us with test kits."

Twenty-six of 120 patients who were residing at the nursing home as of Feb. 19 have since died, with 13 of 15 autopsies carried conducted to date confirming coronavirus was the cause, Life Care officials said on Monday. Among 53 residents still in the facility as of Monday, results for 31 out of 35 tested have so far come back positive for the coronavirus, they said.

The Seattle-King County Public Health agency on Monday reported three more Life Care residents had died from coronavirus infections at local hospitals in recent days, raising the statewide total to 22. But it was not immediately clear whether those fatalities were already included in Life Care's own latest figures.

Washington as a whole has documented 162 confirmed cases, one of the largest tally of any single U.S. state. The nationwide number has surpassed 600.

The outbreak has shown how quickly coronavirus can spread through elderly residents with weak immune systems and underlying health conditions living in close quarters.

"We've had patients who, within an hour's time, show no symptoms to going to acute symptoms and being transferred to the hospital," Killian told a news conference on Sunday. "And we've had patients die relatively quickly under those circumstances."

Two other nursing homes in the greater Seattle area have reported that at least two residents and one staff member have the virus.

Killian said he was not sure whether nurses who worked at Life Care Center Kirkland also worked shifts at other nursing homes in the Seattle area before the outbreak came to light over a week ago.

The University of Washington School of Medicine said on Monday it could test all Life Care staff. The lab's current testing is running at about 500 specimens a day, but it has capacity for over 1,000 tests a day.

"We're happy to perform testing if they can get samples and send them through the University of Washington Department of Laboratory Medicine," said Alex Greninger, assistant director of UW Medicine Clinical Virology Laboratories.

He did not know why Life Care had not received kits, but said a general reason why testing was not higher was a shortage of people to pick up specimens and bring them to his university lab.

(Reporting by Andrew Hay in New Mexico and Deborah Bloom in Seattle; Additional reporting by Steve Gorman in Los Angeles; Editing by Peter Cooney and Michael Perry)

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