RICHMOND — The presidents of three of Virginia's largest public universities have asked the state to set aside $200 million to increase testing for the novel coronavirus on college campuses and elsewhere, arguing that the funding will be crucial to resume higher education and other activities in the coming year.

“In our shared view, expanded testing and the associated costs are unavoidable. Prompt action will allow both for more effective implementation of such testing and for more efficient management of the potential costs,” James E. Ryan of the University of Virginia, Michael Rao of Virginia Commonwealth University and Timothy Sands of Virginia Tech wrote on June 8 in a letter to state Health and Human Resources Secretary Daniel Carey.

Days later, U-Va. officials sent the state further documents explaining that most of the funding — $158.6 million — could be reserved for a massive public health effort to screen students, employees and others for the virus at public and private col­leges across Virginia.

The plan asks the administration of Gov. Ralph Northam (D) to cover the expenses with federal coronavirus relief funds and suggests the universities would carry out the tests in coordination with the state health department.

Northam administration officials said Thursday that they are considering several routes for increasing testing. They questioned whether the scenario outlined by the universities was too broad to meet the federal guidelines that allow the state to pay for it with money from the Coronavirus Aid, Relief and Economic Security (Cares) Act passed by Congress.

“The question will not be whether or not we should do testing. The question is under what circumstances should testing be done, not only for health purposes but also what is reimbursable under the Cares Act,” said state Finance Secretary Aubrey Layne.

Colleges nationwide are racing to determine how much coronavirus testing they need to open campuses safely, and how they will pay for it. There is general agreement that schools must be prepared to test students, faculty and staff who show symptoms of the coronavirus. But there is no consensus on exactly how much they will need to test asymptomatic students and others to protect public health.

“That is the million dollar question — what threshold is safe to reopen,” said Jean E. Chin, an associate clinical professor of medicine at the University of Georgia who chairs a covid-19 task force for the American College Health Association. The situation is fluid because researchers are constantly gathering new data on a pandemic blamed for the deaths of at least 120,000 Americans.

Northam has released guidelines that allow campuses to reopen with some virtual instruction, limits on class sizes, continued social distancing and steps for hygiene. Each college or university must submit reopening plans for state approval.

The guidelines offer no firm rules for testing students or faculty, instead urging schools to work with local health officials on their approach. University leaders argue that testing is key to both managing the virus and ensuring confidence among returning students.

Because “multiple states have relaxed social distancing and quarantine measures in ways that likely increase the risk of further viral transmission,” welcoming students and faculty back to college this fall represents “one of the most challenging examples of resumption of normal activities,” K. Craig Kent, U-Va.’s executive vice president for health affairs, wrote Carey on June 17.

Nationwide, universities’ testing plans vary widely. In Georgia, Emory University aims to screen students for the virus before they move into campus housing. The University of California at San Diego plans to test most students on campus monthly. Purdue University in Indiana plans widespread testing and contact tracing. Schools are also talking about monitoring wastewater and other methods to detect viral hot spots.

“All of us may do something a little different,” said Michael Friedlander, vice president for health sciences and technology at Virginia Tech. He said many schools will focus on testing high-risk campus populations, with “a certain amount” of testing needed for public health surveillance.

U-Va. officials are still mulling their strategy. “Our preference is to test all students,” said Mitchell Rosner, chair of the U-Va. department of medicine. U-Va., VCU and Virginia Tech have coronavirus testing facilities that serve not only their campuses but also the general population in surrounding regions.

The documents U-Va. sent to Richmond describe an initiative to help colleges statewide reopen. A spokesman for the university said the scenario is not a specific proposal but is intended to show how expensive any path is likely to be.

It posits 20 weeks of testing during both the fall and spring semesters, with special emphasis on the three weeks at the beginning of each. During those initial periods, campuses around the state could need 19,700 tests per day. That’s nearly double the 10,000 daily tests Virginia now averages statewide.

The Cares Act sent about $3.3 billion to Virginia to offset expenses directly related to the pandemic. Of that amount, $200 million went to Fairfax County, the most populous and hardest-hit jurisdiction in the state. Other localities have gotten a total of about $650 million, and the state has spent some of the money itself, leaving roughly $1.1 billion to be allocated.

There are 430 outstanding requests for that remaining money, said Layne, the state finance secretary, and the universities’ proposal is among the most costly.

The catch is that the Cares money has to be spent on ex­penses that fit federal definitions as being directly tied to the pandemic. Layne said his concern is that guidelines from the Centers for Disease Control and Prevention outline testing protocols for people who show symptoms or who might have come in contact with an infected person. They don’t cover situations as broad as those described by the universities.

“If you’re following CDC guidelines you have good assurance. If not, then you’re in a gray area of whether or not it’s directly related to covid-19,” he said.

While Virginia has come under criticism for lagging behind other states in its coronavirus testing, the rates of infection have been trending sharply downward in recent weeks. The seven-day average of tests that come back positive is at 6 percent, among the lowest in the country.

The letter from Kent acknowledges the “significant costs” of the universities’ proposal but says that if a vaccine is developed or if lower-cost testing becomes available, expenses would be cut.

The proposal suggests that colleges and universities face significant financial risks that might outweigh the cost of testing. If even 10 percent of the student population decides not to enroll, that could mean a loss for col­leges of nearly $527 million in tuition for the coming school year, according to the proposal.

Layne said he’s well aware of that challenge. But some municipalities are also under financial stress, he said, and the economic hit of the pandemic is going to hurt state agencies across the board. Northam has said he’ll call a special session of the General Assembly in August to address the state’s budget, which legislators froze earlier this year because of the health crisis.

“I am sure we’re going to have to look at our core finances and make some hard decisions,” Layne said. “That’s not to say we’re not going to help higher ed; that’s an important part of not only our education system but our economy. But I don’t think there’s going to be enough revenues without us all making some sacrifices. . . . We are looking at a tough year.”