Coronavirus infections in Hawaii reached their second-highest daily level Thursday as Oahu began complying with a two-week stay-at-home order limiting business and activities on the island.

While state health officials reported 306 new cases, a high positivity rate and a record single-day reporting of four deaths, U.S. Surgeon General Jerome Adams warned that Oahu virus numbers likely will continue to spike.

Adams, speaking at a press conference at Kalakaua District Park along with Honolulu Mayor Kirk Caldwell and Gov. David Ige, said Thursday’s new cases were probably generated a week or two ago and do not reflect the thousands of tests administered Wednesday and Thursday during Oahu’s new two-week surge testing program underwritten by the federal government.

The results of the surge tests, he said, are expected to come back to Hawaii from a lab in California two to three days after they are taken.

“You may continue to see cases and positivity go up over the next week or so,” Adams said. “That doesn’t mean you aren’t doing the right thing. It means we need to continue to do the right things, and in seven, 14 and maybe closer to 21 days, you’ll start to see those numbers come back down again.”

Ige said Hawaii could see positive cases double or even go higher if Oahu reaches its target of an additional 5,000 tests per day under the surge program.

“I just want to prepare people for those numbers. We do expect it. We’re not afraid of it. But we know we’re better off to know where the positives are than to sit and not see them,” Ige said.

Hawaii’s daily new-case count hit triple digits for the first time in late July and remained there this month, with the vast majority of confirmed infections on Oahu. On Aug. 13, the state’s daily new-case count reached a record 355.

On Thursday health officials announced four more virus-related deaths — three women and one man, all from Oahu and all who had been hospitalized with underlying medical conditions.

Two of the women were in their 70s, while the other woman and the man were in their 80s. No other details were provided. The coronavirus death toll in Hawaii now stands at 55.

Thursday’s positivity rate — the percent of positives compared to all tests taken — was 12.35%, Adams said, which puts the state in the red zone (above 10%), a position where too many tests are returning positive.

But state health officials later pointed out that the rolling seven-day positivity rate is only 6.4%, which is in the yellow zone (between 5% and 10%). Johns Hopkins University on Wednesday put Hawaii’s seven-day rate at 8.1%.

Adams said Hawaii should be aiming for positivity rates below 5%, which is the green zone. The surge testing, he said, will help the state identify where the disease is on Oahu and ultimately help push the state’s positivity rate in the right direction.

Officials said a combined 4,800 people were tested Wednesday on the first day of surge testing at Kaneohe Regional Park and Leeward Community College.

Nearly the same number preregistered for testing Thursday at Ewa Mahiko, Waianae and Kalakaua district parks, they said.

The test sites on Thursday appeared to be nearly as popular as they were on Wednesday, when thousands waited in line and many were turned away. Hundreds of cars were seen wrapped around Ewa Mahiko District Park at midday Thursday.

Caldwell said a combined 10,821 people registered for testing Wednesday and Thursday, while 1,500 joined in walk-in testing by midday at Kalakaua District Park in Kalihi.

Ige said he and Caldwell were working to figure out a better way to administer the tests so people don’t have to take up most of the day going through the process.

“I think we learned a lot today,” the mayor said.

The testing will continue today at Ewa Mahiko, Kaiaka, Palolo and Waimanalo district parks. Tomorrow it will be at Kalakaua District Gym parking lot, Kalihi Valley District Park, Polynesian Cultural Center, Wahiawa District Park and Mililani District Park.

Scheduled from 9 a.m. to 2 p.m. each day, the testing will continue through Sept. 8. Register ahead of time at doineedacovid19test.com. No health insurance, visible symptoms or doctor’s note is needed. More dates and locations around the island will be announced later, officials said.

One of the sites being considered for use is Aloha Stadium. Another one is the H-3 freeway.

The state announced late Thursday that the freeway would be shut down between Halawa Interchange and the Halekou Interchange to accommodate surge testing Tuesday and Thursday next week, but that it still needs to coordinate the effort with the federal government.

“Testing on the H-3 is a historic, first ever endeavor that will make a significant difference in getting more people tested,” Caldwell said in a statement issued by the state Department of Transportation.

Elsewhere on Thursday, the Department of Health denied accusations by state Auditor Les Kondo that he found little cooperation during his agency’s examination of the department’s much-criticized contact tracing program. Kondo’s report was published Wednesday.

In a statement, the department denied blocking Kondo from accessing its employees.

“To the contrary, the Department’s employees attempted to accommodate the auditor’s very short time frame for interviews, despite the fact these employees are balancing a number of requests on top of their pandemic response duties. Although we could not immediately schedule interviews according to the auditor’s time frame, we only asked for them to be rescheduled. We were therefore surprised to see the report issued yesterday.”

The statement went on to say, in part, that Kondo’s interview requests “came just as the pandemic began to stretch the Department beyond the limits of its human resources.”