Coronavirus cases are on the rise again across more than half of the U.S.

Across the nation, average new cases have climbed three of the last five days.

Many of the recently growing outbreaks across the country are occurring in the Midwest, including Indiana, Iowa, Kansas, Michigan, Minnesota, Missouri, Nebraska, Ohio and the Dakotas. Those states collectively reported more than 7,400 new cases Sunday, according to data collected by Hopkins.

Iowa has reported an average of more than 1,100 new cases a day over the past seven days, more than double from a week ago, according to Hopkins data. Some of that rise, though, is likely because the state began including antigen test results last week. South Dakota has reported an average of more than 290 cases per day over the past week, up over 104% compared with a week ago.

New cases are also still rising in a number of more populous Southern states. Alabama has reported an average of more than 1,400 new cases a day over the past week, up more than 53% from a week ago, according to Hopkins data, and South Carolina has reported an average of over 905 daily infections, up 15% compared with last week.

The steady rise of new cases in these states and others are turning up in the national numbers. New cases nationwide have been on the decline for more than a month, but the rate of decline has slowed over the past few days. Average new cases have hovered between 41,000 and 43,000 over the past week, a level far higher than federal health officials say is acceptable heading into the fall.

The country collectively reported 35,337 new cases on Sunday, according to Hopkins data, but case reporting tends to drop over the weekend with local health departments closed. The seven-day average of new cases per day has risen over the last two days after weeks of decline. It now stands at just over 42,100, down just 1.2% compared with a week ago — more than double the daily average in early June before the outbreak started to pick up speed again, according to a CNBC analysis of Hopkins data.

Over the past seven days, an average of 5.7% of all tests processed each day came back positive as of Sunday, according to data from Hopkins. That's down from 6.1% a week prior, Hopkins data shows. Epidemiologists often point to the percentage of positive tests as a good indicator of the status of an outbreak.

To be sure, the nation is still reporting daily new cases far below the peak of the outbreak in late July, when the country was reporting nearly 70,000 new cases every day. Hospitalizations, which lag behind the trend of new cases, are also down. As of Sunday, states reported 35,730 individuals currently hospitalized with Covid-19, down 9.4% from a week ago, according to data collected by Covid Tracking Project, a volunteer project founded by journalists at The Atlantic magazine.

The worrying trends across the Midwest come about two weeks after Centers for Disease Control and Prevention Director Dr. Robert Redfield said the middle of the country "is getting stuck" when it comes to combating the virus.

"We're starting to see some of the cases now in the red zone areas are falling, but if you look at those states that are in what we call the yellow zone, between 5% and 10%, they're not falling, so middle America right now is getting stuck," he told Dr. Howard Bauchner of the Journal of the American Medical Association. "We don't need to have a third wave in the heartland right now."

In the same interview, Redfield said he'd like to bring the number of daily new cases reported across the country to below 10,000 and the number of new Covid-19 deaths reported each day below 250. 

The recent rise in new cases comes as many of the country's students head back for in-person learning at colleges and K-12 schools. 

"I'd like to say that it's surprising, but it's not," Dr. Christine Peterson, an epidemiologist at the University of Iowa, said of the outbreak in her state. "Both Iowa State and the University of Iowa started on-campus instruction this last week, which means that in the last couple weeks, over 50,000 students have returned to those campuses with bars open and no restriction on gathering."

The University of Iowa reported 130 cases last week after the first week of class. More than 13.6% of all tests came back positive, the university said, adding it still has "adequate isolation and quarantine housing available." Other universities and public school districts across the country have reported worrying outbreaks among their student bodies, prompting some schools to shift to virtual learning from in-person classes.

The recent surge in cases in Iowa prompted Gov. Kim Reynolds to order the closure of bars in some of the state's most populated counties last week. In Johnson County, one of Iowa's most populous areas with over 150,000 residents, more than 22% of all Covid-19 tests are now coming back positive, according to the county. In Iowa City, which is located in the county, the school board voted last week to start classes online only. 

While Peterson applauded the steps as common sense mitigation measures, she said they're "too little too late." She added that with bars finally closed, she's optimistic that Iowa will be able to get a handle on the outbreak. 

The recent uptick in many states is particularly worrying as a holiday weekend and the fall season quickly approach. Dr. Ashish Jha, director of the Harvard Global Health Institute, said he's "nervous" about activity over Labor Day weekend and about the months ahead as the weather turns, flu season settles in and people perhaps let down their guard against the virus.

"I think the fall is going to be a bit of a mess," he said in a phone interview last week. "If Labor Day begins with a 50-person backyard barbecue that turns into a 30-person indoor drinks after the sun goes down, that's going to be a huge problem."

He added that Labor Day could mark the beginning of what may be difficult months ahead. However, he said he does see "glimmers of hope" in recent advances in testing and treatment that could empower local officials to prevent outbreaks and save lives.

"Once you get beyond September, so much is changing so fast. Some part of me keeps hoping that will be okay as time goes along," he said. "But boy, there's a lot of months ahead before this stuff starts getting meaningfully better."

— CNBC's Nate Rattner contributed to this report.