In the event of a dirty bomb or a nuclear meltdown, emergency responders can safely tolerate radiation levels equivalent to thousands of chest X-rays, the Environmental Protection Agency said in new guidelines that ease off on established safety levels.

The EPA’s determination sets a level 10 times the drinking water standard for radiation recommended under President Barack Obama. It could lead to the administration of President Donald Trump weakening radiation safety levels, watchdog groups critical of the move say.

“It’s really a huge amount of radiation they are saying is safe,” said Daniel Hirsch, the retired director of the University...