Florida Governor Ron DeSantis, a vocal critic of Covid restrictions, has said the state can withhold salaries from school leaders who enact mask mandates.
He earlier issued an order against such policies in schools, but some districts have pushed back, saying their pupils must still mask.
The row comes as US schools begin their new academic year, and as Delta variant surges affect younger groups.
There is no evidence the Delta variant is more severe in children.
Multiple states have recently recorded spiking paediatric hospital admissions, though a number of the child patients reportedly have other conditions such as asthma, diabetes or respiratory syncytial virus.
Just 1% of US children infected with coronavirus end up in hospital and 0.01% die, according to the American Academy of Pediatrics.