Texas and Ohio have included abortions among the nonessential surgeries and medical procedures that they are requiring to be delayed, setting off a new front in the fight over abortion rights in the middle of the coronavirus pandemic in the United States.

Both states said they were trying to preserve extremely precious protective equipment for health care workers and to make space for a potential flood of coronavirus patients.

But abortion rights activists said that abortions should be counted as essential and that people could not wait for the procedure until the pandemic was over.

On Monday, Ken Paxton, the attorney general of Texas, clarified that the postponement of surgeries and medical procedures announced by Gov. Greg Abbott over the weekend included “any type of abortion that is not medically necessary to preserve the life or health of the mother.”