Minnesota is continuing on its recent trajectory of relatively low COVID-19 case counts even as hot spots for the new coronavirus start to emerge across the country.

Health officials warned Saturday, however, that it's too soon to say whether Minnesota will avoid the path of Arizona and other states that have recently reported significant increases in cases.

One key distinction is that other states were quicker than Minnesota to ease social restrictions that help control the spread of COVID-19, said Kris Ehresmann, director of infectious disease at the Minnesota Department of Health. So, those states might just be quicker to see the consequences.

"We have had a lot change in our community mitigation measures," Ehresmann said, pointing to moves on June 1 and Wednesday that let some Minnesota businesses resume at partial capacity. "So, we still have a ways to go to be evaluating the impact."

Nine more people have died of COVID-19 in Minnesota, health officials reported Saturday, as the statewide tally of confirmed cases pushed beyond 30,000.

COVID-19 has caused a total of 1,283 deaths across the state, according to data posted Saturday morning by the Minnesota Department of Health. Residents of long-term care accounted for four of the nine newly announced deaths.

The net count for positive test results grew by 377 confirmed cases on a one-day volume of 12,784 completed tests.

Arizona was noteworthy last week not only for seeing more cases, health experts say, but also because a high proportion of tests were coming back positive. The positivity rate in Arizona was 27% compared with just 3.9% in Minnesota, according to the Coronavirus Resource Center at Johns Hopkins University.

"If the positivity is too high, it tells me a state is not casting a wide enough net in order to find infections," said Jennifer Nuzzo, an epidemiologist at Johns Hopkins University. "That makes me call into question the case counts themselves, but it could also foreshadow future cases."

Rising case counts in Oregon prompted the state on Thursday to announce a one-week pause in reopening activities. Hot spots also emerged in Texas, Georgia and Alabama, said Dr. Georges Benjamin, executive director of the American Public Health Association.

Benjamin said he's been paying close attention to Arizona because the state has a large population of retirees 65 and older who are at higher risk for serious illness with COVID-19.

"They were pretty loose in their initial stay-at-home activity," Benjamin said. "And then they opened up pretty quickly."

In Minnesota, Saturday's numbers continued a string of days with relatively low counts for new cases and deaths.

Last week, 113 people in the state died of COVID-19, which was the smallest weekly tally since April. The average on Saturday for new cases over the previous seven days was 382 — the state's lowest reading by that measure in more than a month.

The trends are improving, Ehresmann said, but she still urged caution.

"I don't ever want to not be grateful for a day where we have low case numbers and low deaths — everybody should be happy for every day that happens," Ehresmann said. "It's just that when it is good, we cannot extrapolate that it's going to be like that forever. I think we have to recognize that this is a very fluid situation."

COVID-19 is a viral respiratory illness caused by a new coronavirus that surfaced in China late last year.

Most patients with COVID-19 don't need to be hospitalized, since the illness usually causes mild or moderate sickness.

Saturday's report showed 390 people require hospitalization including 191 people in intensive care. At times in late May, slightly more than 600 Minnesotans were hospitalized with COVID-19 and as many as 263 patients required intensive care.

People at greatest risk from COVID-19 include those 65 and older, residents of long-term care facilities, and those with underlying medical conditions. The medical conditions range from lung disease, serious heart conditions and cancer to severe obesity, diabetes and kidney patients who need dialysis.

On Wednesday, the state launched the latest in a series of changes to reduce restrictions designed to slow the spread of COVID-19. Indoor restaurants, swimming pools, movie theaters and fitness clubs started to operate at limited capacity.

Officials with the University of Minnesota last week announced plans for a near-normal reopening in the fall that includes classrooms, dormitories and common spaces under restrictions for social distancing. As universities across the country consider plans for reopening, they're confronting difficult questions related to the cost of routine testing, said Dr. Michael Mina, an epidemiologist at the Harvard T.H. Chan School of Public Health.

"If you say that you're going to test 5,000 people daily at a test that costs $50 — and these are just an example — that becomes extraordinarily expensive," Mina said during a Friday call with reporters.

Testing could help prevent outbreaks, he said, but there's also a role for widespread use of even simple masks. Mina cited mask-wearing in densely populated Hong Kong as a likely reason for few outbreaks there.

"Mask wearing ... can be a game-changer," he said, "if we as a society collectively decide that we will adhere to those rules."