LANSING, Mich. — Michigan’s seven-day average of daily new coronavirus cases has fallen by more than 1,200 in a week, a sign that the outbreak may be subsiding in a state where infection and hospitalization rates remain highest in the country.

The state health department on Wednesday reported nearly 5,600 cases in the most recent 24-hour period. That brought the seven-day average to 5,742, down from the third surge’s peak of around 7,000 on April 13.

The seven-day average of tests coming back positive, 13.4%, was down from 15.5% a week before.

Gov. Gretchen Whitmer said earlier this week that the “numbers are far too high,” but they appeared to be slowing and death rates are lower than in the last two waves. She has not tightened COVID-19 restrictions but has asked for a voluntary two-week pause on in-person high school instruction, indoor restaurant dining and youth sports to help curb the outbreak.

About 46% of residents ages 16 and older have gotten at least one vaccine dose, including 31% who are fully vaccinated.