“Senior city health officials have expressed to the mayor and his administration their disagreement and concern with using the 3% threshold to close schools in the city, given that schools themselves are not at 3% and that transmission in schools is not as big a concern as it is in other settings like bars and restaurants,” the source said.

De Blasio spokesman Bill Neidhardt said the claim is “not true.”

At a press conference earlier in the day, de Blasio himself did not deny that there have been disagreements within his administration over the use of the threshold, but he and his health advisors provided only a vague picture of what has transpired behind the scenes.

The dispute among top advisors raises the question of why the mayor continues to use that threshold, with some observers speculating that the teachers union has lobbied de Blasio to maintain it. The United Federation of Teachers did not immediately return calls.