WASHINGTON — The government said today that schools should only close this fall if large numbers of students have swine flu, and could allow their sick kids to return 24 hours after a fever is gone.

The decision on closing rests with local school officials, but they have been looking to the federal government for advice about the new flu strain that has caused a global epidemic.

The advice on sick kids returning is a change from previous recommendations that people with swine flu stay home for a week.

As the virus spread to students last spring, more than 700 schools in half the states temporarily closed their doors. The new flu is expected to hit schools again this fall. But the Obama administration is hoping to minimize closings and disruptions they cause for families.

Homeland Security Secretary Janet Napolitano offered the advice on school closings, while the guidance on students returning came from Dr. Thomas Frieden, director of the Centers for Disease Control and Prevention.

Unlike regular seasonal flu, this virus has not retreated during the hot and humid summer months and so far has infected more than 1 million Americans.

“We hope no schools have to close, but realistically, some schools will close this fall,” Education Secretary Arne Duncan said this week during a forum with administration officials that was broadcast online.

“I’m dealing first and foremost as a parent,” Duncan said today on a nationally broadcast news show. “I want to keep my children safe and keep them learning.” He said officials are asking parents to “use common sense” and encourage their children to vigorously wash their hands several times a day and take other safety precautions.

“We want to provide as much facts as we can” to local officials, he said. “Basically, this will be a tiered response. If there’s a handful of children at a school who might be sick, we want the parents to keep them home. If the numbers escalate dramatically, then we might have to close the schools.”

Duncan said officials anticipate the vaccine will be available by mid-October and that they want schools to be principal sites for getting the shots.

Students got an unexpected vacation last spring, but many parents scrambled to find child care.

School officials had been acting on advice from the CDC, which at first said schools should shut down for about two weeks if there were suspected cases of swine flu.

Then the CDC changed course, saying schools did not need to close because the virus was milder than feared. Instead, parents were told to keep sick kids home for at least a week.

Duncan said at a swine flu summit last month that closing school should be “a last resort, not a first resort.”

He said earlier this week that school districts should use common sense. “If you have one child sick, that’s one thing. If you have a whole host of children getting sick, that’s another,” Duncan said.

While this particular flu virus is new, the matter of school closings is not. Every winter, regular flu outbreaks prompt a relatively small number of schools to close for a few days because of high absenteeism among students or staff.

In addition to new guidance for when to close, the CDC and Education Department said this week they have set up a new monitoring system to track school closures across the country.

Still up in the air is whether schools will be turned into vaccine clinics, though Health and Human Services Secretary Kathleen Sebelius has said that seems logical. “We’re seeing schools as potential partners,” she said at the forum with Duncan.

Children are on the priority list for the first doses of swine flu vaccine, but because of time needed for testing and manufacturing, inoculations can’t begin until school has been in session for more than a month; the government is aiming for Oct. 15. Many questions remain, including whether people will need one shot or two for protection. That is in addition to the regular winter flu vaccine that is also recommended for children.

States and school districts should be preparing for the possibility of mass vaccinations, federal officials have said.

They also should make plans to keep kids learning when schools do close, Duncan said.

Duncan was interviewed today on CBS’s “The Early Show.”