The union representing New York City’s public-school teachers said its members would not return to classrooms next month unless the city met their health and safety demands — including testing all students and staff for that coronavirus and ensuring all schools have a nurse.

The announcement from the United Federation of Teachers (UFT), which represents 75,000 professionals, comes a week after Mayor Bill de Blasio announced that schools would reopen Sept. 10 for in-person classes, saying he believed the city’s low positivity rate would allow for students to return safely. The city, once the nation’s epicenter of the pandemic, has a positive test rate of less than one-quarter of 1 percent, the mayor said Wednesday.

UFT President Michael Mulgrew threatened legal action against the city and said teachers would strike if the mayor tried to force them to return to classrooms. And he acknowledged that it would be virtually impossible for the city to meet the union’s health and safety demands before Sept. 10 — making a showdown between teachers and the mayor increasingly likely.

“We have promised the teachers and the parents of New York City that we would stand and fight if we felt a school was unsafe,” Mulgrew said Wednesday, flanked virtually and in real life by doctors and civil rights leaders.

De Blasio, speaking as he toured an elementary school in Brooklyn’s Crown Heights neighborhood, said the city had been working with the union for months and that he hoped the discussions would continue.

“We’re going to work with them regardless of what they say,” de Blasio said, “because we care more about kids and parents than these games.”

Schools across the country are struggling with questions over how and when to reopen classrooms, with nearly all large urban districts choosing to start school remotely over concerns that sending kids back to campuses could contribute to the spread of the coronavirus in their communities. Complicating matters, there is still much that doctors do not know about the virus, including how easily children, who generally experience mild or no symptoms, could transmit it to a teacher.

But, responding in part to pressure from President Trump, several school systems in Georgia, Tennessee, Mississippi and Florida have already opened their doors despite infection rates far higher than New York City’s. A Georgia high school eventually had to shutter for cleaning when students and staff tested positive for the virus. Elsewhere in the state, and in Mississippi and Tennessee, thousands have had to quarantine after being exposed to students or staff who tested positive for the virus.

Trump has called repeatedly for schools to reopen because he views it as essential to restarting the economy and critical for his reelection bid.

De Blasio said last week that he believed it was safe for students to return to class and that parents still had the option of keeping children home for remote learning. About 395,000 families answered a survey about whether they want to send children back to classrooms. About two-thirds of those families said they wanted to keep their children home.

The union’s safety report calls on the school system to allow union inspectors to scrutinize every school building, ensuring there is adequate ventilation, a school nurse, enough space to keep desks six feet apart and enough personal protective equipment. Mulgrew warned that failing to abide by the measures could cause “one of the biggest debacles in history.”

“If we don’t do that, we’re going to have the same stories we’re seeing in Georgia, in Florida, in Mississippi — the same thing will happen here,” Mulgrew said.