OLYMPIA — Gov. Jay Inslee on Tuesday mapped a course for reopening the state and reviving the economy — but cautioned that many restrictions related to COVID-19 will remain past May 4.

Given encouraging signs that the spread of coronavirus is likely in decline, prohibitions could be lifted soon on some elective surgeries, residential construction and much of the outdoor recreation “that is so much a part of our Northwest identity, as well as our physical and mental health,” Inslee said in a televised address.

But moving too fast, too soon to repeal restrictions across the board could be “disastrous” and lead to another outbreak.

“The reality we need to be aware of is simply this: We are going to have to steel ourselves against this virus for quite some time,” Inslee said Tuesday. “It is going to affect our daily lives in many ways for months. And we have to be aware that it could come back at us in waves.”

On Tuesday, the cumulative COVID-19 case count in Snohomish County stood at 2,189 confirmed infections and 175 probable ones, with 98 dead since the outbreak began in January, according to the Snohomish Health District. Statewide, the tally was 12,282 cases and 682 deaths, the state Department of Health said.

The governor spoke two days after 2,500 people demonstrated in Olympia against his stay-home order, which has shut down much of the state since last month. The order remains in place until May 4, although the governor’s chief of staff said as of this week it is likely to be extended through the end of May.

Inslee’s plan focuses on protecting public health, bolstering the welfare of families, phasing in a restart of industries, and preventing the virus from leaving more Washingtonians dead in its wake.

Before social-distancing restrictions are eased, Inslee said there must be sufficient testing and contact tracing — that is, the process of finding everyone who has come in contact with an infected person, so they can be checked and possibly isolated.

The governor reiterated that the state remains “drastically behind on testing supplies,” and he sent a letter Tuesday to Vice President Mike Pence asking the federal government to help by building a “robust national testing system that will enable a safe return to public life amid COVID-19.”

Inslee wrote that Washington was working to procure 2½ million test collection kits, but the state was nowhere near that number Tuesday. In his speech, Inslee said current capacity was around 4,000 tests per day, when it needs to be closer to 30,000.

A number of key questions still need answers, such as what agencies will be responsible for bolstering the contact-tracing workforce, who will train and manage the new employees and — perhaps the biggest question of all — who will pay for the mammoth effort.

Inslee didn’t answer those questions with specifics in his address Tuesday.

“We really can’t let that be a concern. We will find the money,” David Postman, Inslee’s chief of staff, told reporters shortly before the address. If the state doesn’t have enough money, he said, “we’ll go to the federal government.”

Nearly 600 people across Washington are trained to conduct contact investigations, and another 800 volunteers are expected to start soon, said Dr. Kathy Lofy, the state health officer. The state hopes to “scale up” those numbers even more, she said.

Inslee is aiming to get the total number to 1,500 workers by mid-May.