The Trump administration is formally withdrawing federal limits on carbon emissions at power plants, triggering the next stage of what is likely to be a yearslong fight over the government’s centerpiece regulation for slowing climate change.

The move pushes forward on a central pledge of President Donald Trump: a rollback of Obama-era environmental rules he has criticized for harming businesses and coal miners in particular. And it pushes the federal government further away from any effort to combat global warming, following...