MADISON, Wis. (AP) — New federal guidelines that would force international students at the University of Wisconsin-Madison to leave the U.S. or transfer to another college if classes go entirely online this fall has injected another layer of uncertainty for thousands of students.

The national guidelines issued Monday by U.S. Immigration and Customs Enforcement affect all international students attending colleges and universities across the country. It could result in an untold number of international students, many of whom typically pay higher tuition rates, returning to their home country.

There were more than 7,200 students from 134 different countries enrolled at UW-Madison last fall. That is nearly 16% of the 45,000 students at UW-Madison.

“Our university system is internationally recognized,” said UW System spokesman Mark Pitsch. “There’s a good reason students from all over the world want to attend our universities. We welcome them. These students provide great benefit to our universities and anything that makes it harder for them to attend will raise a host of issues during an already challenging time.”

UW-Madison spokesman John Lucas had no immediate comment. Samantha McCabe, the director of International Student Services at UW-Madison, declined to comment and referred questions to the university’s public affairs office. The American Council on Education, which represents university presidents, on Monday called the guidelines are “horrifying” and said they will result in confusion as schools look for ways to reopen safely.

Gov. Tony Evers, who previously served on the UW Board of Regents, raised concerns about the guidelines when asked about them during a news conference Tuesday.

“I get the interest in making sure that people have a face to face opportunity to interact with teachers, professors or whatever,” Evers said. “But there may be situations where it just can’t happen because of a surge or because of several issues making things more complex.”

UW-Madison currently plans to offer both in-person and online classes in the fall. However, after Thanksgiving all classes will be offered online and large lectures will all be online the entire semester. Other UW campuses, as well as other colleges and universities throughout Wisconsin, have taken similar approaches for the upcoming academic year.

Under the updated rules, international students must take at least some of their classes in person. New visas will not be issued to students at schools or programs that are entirely online. Students aren’t exempt from the rules even if an outbreak forces their schools online during the fall term.

The guidelines put pressure on UW-Madison and colleges across the country to reopen, as President Donald Trump has called on them to do. But in recent weeks, COVID-19 cases have been spiking in Wisconsin, particularly among college-age students. Last week, Public Health Madison & Dane County closed all bars, except for take out, amid a spike in cases. On Tuesday, it announced that everyone in the county will be required to wear masks while indoors starting on Monday.

From June 13 through June 26, almost half of the 614 people who tested positive for COVID-19 in Dane County were between the ages of 18 and 25 years old. Of these cases, 132 were associated with people at bars.

The new guidelines affecting international students come as President Donald Trump insists that schools and colleges return to in-person instruction as soon as possible.