More and more state and local leaders are making similar requirements. In Indiana, masks will be required starting Monday. In Minnesota, the governor is mandating that people wear masks indoors in businesses and at public settings effective Saturday. And the mayor of Washington, DC, just made the district's mandate stricter.

"We've got to get this virus under control, wearing masks is going to make a difference," DeWine said at a press conference. The mandate goes into effect at 6 p.m. Thursday.

The announcements come a day after President Donald Trump stressed the importance of wearing masks to tamp down the coronavirus.

At least 41 states plus Washington, DC, and Puerto Rico now have some type of mask requirement order in place.

Until now, Ohio had only mandated that residents in counties at a "red" and "purple" risk level wear masks.

The University of Washington's Institute for Health Metrics and Evaluation projects there will be about 5,000 fewer US deaths from Covid-19 by November 1 than it did in its earlier model, partly because of the increasing mandates for people to wear masks and the rising number of people wearing them, even when not required by law.

The mandates come amid an explosion of Covid-19 cases in the Sun Belt, with some states reporting record-breaking numbers of new cases and many hospitals are running out of intensive-care unit beds.

More people are wearing masks in those states, including Florida, California, Texas and Arizona, that have seen a recent spike in cases, said Ali Mokdad, a professor of health metrics sciences at IHME.

But the states that have mask mandates have seen more universal adoption, he said.

"So a mandate is very important and helping, and a national mandate, of course, would do much better," Mokdad told CNN.

'One of the best tools'

"Until there is a widely available vaccine, wearing a mask is one of the best tools we have for limiting the spread of COVID-19 and its harmful impacts," Minnesota Department of Health Commissioner Jan Malcolm said in a release announcing the state's new mandate.

In Washington, DC, Mayor Muriel Bowser announced a new order requiring residents to wear masks outside of the home, even for children as young as 3 years old.

"Basically, what it says is, if you leave home, you should wear a mask," Bowser said at a news briefing.

Wearing a mask now will shape what Ohioans will be able to do in the coming months, the governor said.

"It will make a difference in what our fall looks like," DeWine said.

"We all want kids to go back to school, we want to see sports, we want to see a lot of different things. We want to have more opportunities in the fall and to do that, it's just very important that all Ohioans wear a mask," he said.

CNN's Rebekah Riess, Jen Christensen, Raja Razek, Eileen McMenamin, Ali Main and Lauren Koenig contributed to this report.