In addition, state Attorney General Bob Ferguson filed a motion Friday asking the high court to delay the effect of its decision by 120 days so the state can implement a plan to ensure alternative care is available.
On Aug. 7, the Supreme Court ruled that the practice known as "psychiatric boarding," or holding mentally ill patients in emergency rooms, was unlawful. The state estimates the ruling applies to about 200 people.
The state's understanding is that is has until Aug. 27 to move the patients.
Jane Beyer with the state Department of Social and Health Services said 10 beds have already been secured at Eastern State Hospital. With Inslee's help, the agency has identified and secured funding for as many as 145 more beds, she said.
Fifty of those beds will be available within 20 days, and 95 additional beds will be available in the next 120 days, Beyer said.
"We are working as quickly as we can to find beds and resources for impacted patients. These additional beds are an essential interim step as we work on a long-term solution," the governor said in a statement.
Beyer said the request for a stay "does not challenge the upper-court ruling, it simply asks for more time as it will take several months to open enough evaluation and treatment beds to accommodate the current demand."
Ferguson said "a broad coalition" of hospitals, health care organizations and disability rights groups joined in his motion.
"My office wants to ensure the state is able to implement the court's decision in a way that protects vulnerable individuals, public safety and health care providers," the attorney general said in a statement released Friday evening. "No one would benefit from the release of people in mental health crisis without treatment. We hope the court will see the broad consensus in support of this motion and grant it."
The justices ruled that mentally ill patients who are involuntarily committed cannot be "warehoused" in emergency rooms or acute care centers as a way to avoid overcrowding certified mental health facilities. Patients have a right to adequate care and individualized treatment, and state law required they be detained in certified evaluation and treatment facilities, the court said.
The state's involuntary-treatment law passed in 1973 allows people to be committed to a mental hospital or institution against their will for a limited period of time. The purpose is to evaluate and treat people with a mental disorder who may be gravely disabled or pose a danger to themselves.
The state has been using "single-bed certifications" as a way to temporarily hold involuntarily committed people in hospitals that aren't certified to evaluate or treat their mental illness.
Beyer said the extra time requested will enable the Department of Social and Health Services to work with the governor's office and the Legislature, legislative staff, Office of Financial Management and private care providers to develop a long-term solution to the shortage of psychiatric care.
The department's mental health program will have to seek a supplemental appropriation in the 2015 budget to avoid other mental-health reductions in this fiscal year, the agency said.