The rate of diagnostic tests finding infections with the coronavirus that causes COVID-19 has increased in Minnesota above 5%, a key threshold to public health authorities.

Testing identified another 606 infections that were reported on Tuesday by the Minnesota Department of Health along with four deaths.

The state also reported that 328 people were hospitalized for COVID-19, and that 159 needed intensive care due to breathing problems or other complications. Both numbers are below their daily highs in late May in Minnesota, but reflect a resurgence in COVID-19 hospitalizations since mid-June.

Minnesota has been reporting an increase over the past month in both the number of COVID-19 diagnostic tests and in the rate of those showing positive results. That rate had been as low as 3% in mid-June, but state Health Commissioner Jan Malcolm on Monday said it was now 5.1%

The Johns Hopkins Coronavirus Resource Center lists 16 states, mostly in the northeast, with rates below the 5% threshold and 34 states with rates above it.

Mississippi has a testing positivity rate amid rising COVID-19 case counts in the South of 23.3%, while Vermont has a rate of .4%, according to Johns Hopkins.

Malcolm said the positivity rate is an indicator of concern about the direction of the COVID-19 pandemic, and she urged people to continue following state guidance over wearing masks, practicing social distancing, covering coughs and staying home when sick. She and other health officials expressed concern over mass group events such as the upcoming Sturgis motorcycle rally in South Dakota.

“Every time each of us makes a decision that makes transmission more likely,” she said, “we’re really holding back the rest of our state from moving ahead toward ... the better days we are all so eager to reach.”

Three of the deaths reported on Tuesday were in Scott County — all in people 50 or older. The fourth death involved a person in the 60 to 69 age range in Hennepin County. The death toll for the pandemic in Minnesota is now 1,620.

The state has reported a total of 57,162 infections with the SARS-CoV-2 virus that causes COVID-19, including 50,426 who have recovered to the point they are no longer considered infectious or required to isolate themselves.

Studies have found that a substantial share of patients suffered lingering breathing or health problems in the weeks following their infections.

Even among patients who received only outpatient care, 35% weren’t back to usual health two to three weeks after they first experienced symptoms, according to a national study published by the U.S. Centers for Disease Control and Prevention last month. Hennepin Healthcare contributed patient data to that study.