Honolulu Mayor Kirk Caldwell said Tuesday that he is extending Oahu’s stay-at-home, work-from-home order “with modifications” through May and is reopening city parks — for exercise only — beginning at 5 a.m. Saturday.

He also announced a $2 million program for 10,000 more COVID-19 tests to be conducted by community centers around the island that provide health care for underserved populations.

Caldwell’s original stay-at-home, work-from-home order was set to expire at the end of the month. It requires most businesses to close to the public, leaving only essential businesses such as supermarkets and restaurants, which can’t offer sit-down service.

Asked Tuesday to address those who have been furloughed or laid off and want the sheltering-in-place orders lifted sooner, Caldwell said, “We are taking the first steps toward getting them back to work.”

Caldwell said some additional businesses may be allowed to open before May 31 if it is safe to do so. “If this (the amount of new positive coronavirus cases) stays low, we can start talking about opening up other things, too — in a phased way,” he said.

Among the first operations that may be allowed to open in the near future: car dealerships and real estate companies, but by appointment only. “It could mean small retail under 50,000 square feet, only half the capacity of the store under the fire code … everyone wearing masks, both employees and customers,” Caldwell said.

The idea is to slowly reopen segments of society as safety allows, “and at the end of the day, the order will disappear and we’ll return to the life we lived before the pandemic struck.”

He said he expects sports or other entertainment events may be the last to reopen because they entail large numbers of people gathering. “That doesn’t mean … we’re not going to see sports won’t be played, but we’ll be watching from afar, from our TV screens, but not in person sitting in bleachers.”

Caldwell said the city’s 300 parks will reopen Saturday, but only for running, jogging, biking, walking and other exercise that allows for safe social distancing. Picnicking, team sports from basketball to tennis to pickleball, swimming in city pools and use of playground equipment are disallowed because they carry a larger potential for the spreading of COVID-19, he said. “This is all about physical distancing.”

The park’s restrooms and parking lots will be open.

The city’s five botanical gardens will open May 1, the mayor said. Hanauma Bay and Koko Head Shooting Complex will not reopen.

Caldwell said he is reopening the parks on the advice of an advisory group of physicians and psychiatrists. “People have been cooped up, they feel anxious. The only thing they can do now to get exercise is to walk or run on a city street or state road, and that’s not ideal,” he said.

As many as seven Oahu community health centers that care for underserved populations are participating in the coronavirus testing program. The four that have agreed in principle to having testing set up at their sites are the Kalihi-Palama Heath Center, Wahiawa Center for Community Health, Waikiki Health and Koolauloa Health Center. In discussions to do the same are the Waianae Coast Comprehensive Health Center, Waimanalo Health Center and Kokua Kalihi Valley Health Center.

The city will pay for the test kits as well as for the testing to be conducted, Caldwell said. The health centers are also being provided with personal protective equipment for those conducting the tests.

Those found to be positive would need to self-isolate. “If they can’t be cared for in their homes because they’re multigenerational, the city’s prepared to enter into an agreement with a small hotel chain in Waikiki that would allow them to stay in the rooms for free — for those who cannot stay with their family,” Caldwell said.

Each center is also being given $20,000 to develop telehealth care infrastructure “so that they can talk to their patients online and not require them to come in and be talked to,” the mayor said.

Some of the centers already are conducting COVID-19 testing.

Dr. Vija Sehgal of the Waianae Coast facility said 20-25 tests are conducted there daily, by appointment only. About 650 tests have been conducted, with four showing positive results, Sehgal said. Among people now being tested are those who’ve come in contact with someone who’s tested positive, even if asymptomatic, as well as those showing symptoms including the loss of taste or smell, she said.

“We keep loosening up our criteria,” Sehgal said. “As testing swabs become more available, we have become less stringent.”

UPS is providing delivery and collection of the tests as part of a national program. The new testing is expected to begin next week, and the city has been promised it will get results within 48 hours, Caldwell said.

Councilman Joey Manahan said UPS also donated to the city 20,000 N-95 masks for Honolulu’s first responders. The city had been having trouble procuring masks because it needs to bid with other state and municipal governments for the equipment, he said.

Caldwell said the $2 million for the program is “a small price to pay” for ensuring the community is safe before different segments of society are reopened. “That small investment can pay gigantic dividends,” he said. “And we’ll spend more if necessary.” The $2 million had previously been allocated for replenishing sand at Ala Moana Regional Park, he said.

Last week the city announced it is receiving $387 million in cash under the federal government’s $2.2 trillion Coronavirus Aid, Relief and Economic Security package. Caldwell said Tuesday he will announce shortly how that money will be spent. The CARES Act requires the money to be spent on efforts to curb the pandemic and must be used by the end of the year.