Ms. Haaland, one of the first former cabinet officials in the Biden administration to announce a run for office, would be the first Native American woman to serve as governor of a state.

Haaland has served in Congress and as interior secretary in the Biden administration, and she is now hoping to become governor of New Mexico.

New Mexico Sen. Martin Heinrich on Thursday declined to endorse former Interior Secretary Deb Haaland’s gubernatorial bid, just weeks after the top Energy and Natural Resources Committee Democrat backed out of a potential run himself.