The number of identified coronavirus cases in Hawaii inched upward to 586 Tuesday based on two new positive test results, while the number of COVID-19 deaths in the state reached 12.

Two men who had coronavirus and underlying health conditions died late Monday night, state health officials said. The deaths, both men who were 65 years old or older, occurred on Oahu and Maui, officials said.

“We are saddened by these additional deaths and the toll the pandemic is taking on the families and friends of those affected,” said Gov. David Ige in a news release announcing the deaths. “This is a serious disease especially for those with pre-existing health conditions and older adults. It is critical that we all comply with the stay at home order, practice social distancing, and continue to wear a mask whenever we go out to protect others.”

The Maui death was the fifth for that island, and Maui Mayor Michael Victorino released a statement Tuesday saying that “Joycelyn and I extend our deepest condolences to the family and friends of this Maui County resident. We mourn for each and every person lost to this virus, and ask the community to surround each family with love and support.”

The new data released by the state Health Department marked the second straight day that Oahu reported no new cases, and the two cases were the smallest number of new cases statewide since March 18. Both of the new cases were reported on Maui.

Tuesday marked the third consecutive day that fewer than 10 new cases were reported for Hawaii, which as of Monday was tied with Montana for the lowest infection rate in the nation. Hawaii also ranked among the eight states with the lowest COVID-19 death rates as of Tuesday.

The man who died on Oahu had underlying health conditions and was hospitalized in late March. He recovered and was discharged, “but his health subsequently declined and he passed away at home yesterday,” state officials said.

The man on Maui also had underlying health conditions, state officials said. “He had been in the hospital at Maui Memorial Medical Center since late last year. This person’s death is considered related to the MMMC cluster, which as of yesterday had 36 staff and 20 patients under investigation as potentially associated with the cluster,” health officials said.

The Health Department provided no other details on the two men.

On Hawaii island, civil defense officials announced that 32 of that island’s 63 identified cases stem from a single cluster that has been linked to McDonald’s restaurants on the west side of the island. None of the cases involve customers of the restaurants, according to the Health Department.

“The very hard lessons learned, and we should all learn is (the) critical importance of following the health advisories of stay at home if you are sick, physical distancing, face coverings and (avoid) social gatherings,” according to the message from the Hawaii County Civil Defense Agency.

Two of the cases were detected by testing nonsymptomatic family members associated with the fast food restaurant cluster, which “clearly illustrates that anyone can be a carrier without knowing it. All are strongly recommended to wear a face covering. This is a community issue and we all need to do our part,” according to the Civil Defense statement.

Hawaii County Mayor Harry Kim issued a new rule Tuesday that mandates face masks or coverings for all customers of essential businesses who are age 5 or older, and for all employees who deal with the public. The rule also calls for all customers to sanitize their hands at hand sanitizing stations to be set up at business entrances.

The new rule requires businesses to refuse entry to anyone who refuses to wear a face mask or face covering. Customers with health or medical conditions that prohibit the use of face masks or face coverings are exempt.

As of Monday the statewide count of coronavirus cases was 586, and of those cases, 437 have recovered and been released from isolation, for a recovery rate of more than 74%.