The union representing Philadelphia public school teachers said Monday that it supports a vaccine mandate for school employees, paving the way for such a requirement as students return to classrooms later this month.

“The union has never, and will never, stand in the way of the health and safety of educators and students alike,” Jerry T. Jordan, president of the Philadelphia Federation of Teachers, said in a statement.

Jordan’s announcement came hours after Superintendent William R. Hite Jr. and Mayor Jim Kenney said they were continuing to discuss the possibility of requiring vaccination for school and city employees. Debates over such mandates — which are now in place for government workers in several cities as well as the federal government — have taken on additional urgency amid a surge in coronavirus cases nationwide and as schools prepare to reopen.

“Everyone should be vaccinated — I don’t know how else to say it,” Kenney said, raising his arms in exasperation as he spoke Monday morning at a back-to-school event in Northeast Philadelphia. “I don’t want to twist anybody’s arm to do it, but we’ll try to figure out a way to get people to cooperate.”

How that might occur remained unclear: As of Monday, none of the four labor unions representing thousands of city workers has come out in support of a mandate. One said there have been no discussions with City Hall.

Still, discussions are playing out across the region as coronavirus cases surge due to the delta variant, the highly contagious form of COVID-19 that has been both detected in and spread by vaccinated individuals, even though they are far less likely to get seriously ill than unvaccinated people. In New Jersey, which already has a mask requirement in place for students and staff returning to schools, Gov. Phil Murphy said Monday he was “looking at all options” for requiring vaccines and hopes to have an announcement in a few weeks.

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The New Jersey Education Association, which represents thousands of public school teachers, signaled it would support vaccination for its members, noting in a statement that the union “will work to ensure that it is implemented in a way that protects the health and welfare of everyone involved” if Murphy mandates vaccines for school staff.

Pennsylvania Gov. Tom Wolf, meanwhile, has shown no signs of going in that direction. Last week, Wolf announced he would not even require masks in schools, instead leaving the decision up to individual districts. He also governs in a different political landscape than his Democratic counterpart in New Jersey: Wolf has faced backlash from the state’s Republican-controlled legislature over his previous coronavirus restrictions, and voters approved a referendum in May limiting his emergency response powers.

At Monday’s event, Hite said he isn’t concerned that the School District will need to shift to virtual or hybrid learning as the delta variant spreads, noting that the district’s safety measures follow guidance from the Centers for Disease Control and Prevention. The district will require masks and mandate weekly testing for teachers as well as for students showing symptoms.

But he said vaccine mandates are a “complex” issue.

“I would have mandated it a long time ago,” Hite said. “The unions have also been very supportive of getting their individuals the vaccination, and so it’s just something we’re continuing to work through.”

Among other issues, Hite said there is concern that a vaccine mandate could exacerbate the existing shortage of bus drivers, food workers, and clerical staff. And those staff members are represented by other labor unions with which the district would also have to discuss a mandate. Those unions did not respond to a request for comment Monday.

Hite and Kenney spoke at the first stop of a back-to-school bus tour at Jardel Recreation Center in Northeast Philadelphia, where families lined up around the block to receive backpacks and other gear, as well as enrollment information.

“I’m excited but nervous, of course, because COVID is still around,” said Siani Alderman, whose son Christopher is beginning kindergarten this year.

Alderman said her son, who got a new blue backpack at Monday’s giveaway, is excited to go to school and make friends. But she said she worries about his health because he is too young to be vaccinated.

“Hopefully they’re taking the proper precautions,” she said of the School District.

Jordan said the teachers’ union supports a mandate as long as it includes exemptions for religious or health reasons and is negotiated through the collective bargaining process. He also said weekly testing should be required of students in addition to teachers.

Kenney acknowledged a vaccine mandate is “an HR issue” that requires discussions with the city’s workforce.

“You don’t just tell people you’re going to do this or that,” he said, “without having a discussion with them.”

Those discussions are ongoing, he said. But through Monday, none of the four labor unions representing municipal workers has come out in support of a mandate.

“The mayor hasn’t said a word to me about it,” said Michael Bresnan, president of Local 22 of the International Fire Fighters and Paramedics Union. And a spokesperson for the Fraternal Order of Police Lodge 5 declined to comment Monday. Both of those unions previously reported low vaccination rates among their members.

A spokesperson for AFSCME District Council 33, which represents blue-collar city workers, also declined to comment. And the president of District Council 47, which represents white-collar employees, did not respond to a request for comment Monday.

The largest union representing New Jersey state workers, the Communications Workers of America, has not said if it would oppose a possible vaccine mandate. Last week, after Murphy said he would mandate vaccines for health-care workers, AFSCME New Jersey, which represents nurses, corrections officers, child care providers, and sanitation workers, said the governor agreed to bargain with them over the matter.

“We strongly encourage all New Jersey citizens, including AFSCME New Jersey members, to get vaccinated as soon as possible. This is in everyone’s best interest,” the group said in a statement last week. “We hope Gov. Murphy’s willingness to bargain with us serves as an example to other employers across the state who intend to mandate the vaccine or weekly testing.”

Staff writers Sean Collins Walsh and Melanie Burney contributed to this article.