The state is undergoing a test of its ability to respond to potential outbreaks of the new coronavirus after a recent spike in the number of cases, Honolulu Mayor Kirk Caldwell said Sunday.

“This is the first test, as we see an increase,” he said Sunday morning, after the state had two consecutive days of double-digit increases in new coronavirus cases. “If (state health officials) are really on it, just like South Korea, just like Seoul, we should be able to bring it down. That’s what we are looking for in the next couple of days.”

Caldwell was referring to the 15 new cases Friday and 17 cases reported Saturday, which were the biggest single-day increases in the islands in nearly two months. Twelve of the cases from Friday and Saturday, however, involved only one household in Waipahu.

Later Sunday the state Department of Health reported five new cases, raising the statewide total of infections to 728. Sunday’s cases included four on Oahu and one on Hawaii island — that island’s first case in 2-1/2 weeks.

State Health Director Bruce Anderson told the Honolulu Star-Advertiser on Sunday that two cases on Oahu were travelers from Washington state and California, and both were in isolation.

Of the two other cases on Oahu, one involved a person at a low-income housing project who was a close contact of another person who had previously tested positive. The last person who tested positive on Oahu took a coronavirus test before a medical procedure, Anderson said. The state is still investigating that case.

On the Big Island the resident who tested positive lives on the island’s east side and was connected by contact tracing to a previous case in March, Anderson said. Hawaii island officials reported that the new case “seems to be very isolated and connected to a previous travel-related case.”

Meanwhile, the state announced a new website where travelers can download the mandatory interisland travel and health form in preparation for interisland travel without the mandatory quarantine to begin Tuesday.

The state urged travelers to arrive at the airport early — similar to traveling after Sept. 11, 2001 — with time to clear health screenings, which include turning in the travel form and a thermal screen. Anyone who doesn’t provide the form or has a temperature greater than 100.4 degrees will not be allowed to fly.

While the interisland quarantine is coming to an end, the two-week quarantine for out-of-state visitors remains in place until July 31.

Caldwell said he plans to speak with the other county mayors about easing trans-Pacific travel. He said under his model, those who don’t do a test before arriving should be required to get a test in Hawaii and quarantine until they get a negative result.