EDEN, N.C.—Beneath the surface of the Dan River, which flows along the foothills on the Virginia state line, lie the soggy remnants of a coal-ash spill that is roiling the political landscape in the state and the regulatory environment nationwide.

A metal pipe running underneath a 58-year-old waste-storage pond owned by Duke Energy Corp. burst Feb. 2, pouring as much as 39,000 tons of coal ash—the byproduct of burning coal for fuel—into the adjacent river. Now, North Carolina's governor and Duke are at odds over the energy company's obligations to clean up the spill and to remove or remediate coal ash in 32 other such storage ponds in the state.

A federal grand jury is scheduled to convene Tuesday in Raleigh to question Duke and state regulators about oversight of the pond as part of a criminal investigation by the U.S. attorney's office for the Eastern District of North Carolina. Prosecutors are reviewing records, photos and emails exchanged between Duke and state regulators about the spill. Duke said it is cooperating in the investigation.

Duke Chief Executive Lynn Good said in a cleanup proposal submitted to the state Wednesday that the company would move the ash at the Dan River site to a landfill lined to prevent seepage of pollutants. She said Duke is also committed to safeguarding its other sites, though it could take years. There would also be an untold cost to remove the ash from sites that have had documented structural problems and to drain many others. "We want to get the near-term and long-term strategies right and implemented in a timely way," Ms. Good said.

But Republican Gov. Pat McCrory says Duke should create lined landfills for all its coal ash in the state. Mr. McCrory's administration criticized Ms. Good's four-page proposal as lacking detail and "inadequate" because it addressed only a handful of Duke's coal-ash ponds. Mr. McCrory, a former Duke executive who has been criticized by environmentalists and Democrats for his onetime ties to the company, has been tough on Duke's pond maintenance and response in part because he knows Duke well, spokesman Josh Ellis said. "He knows how processes are supposed to be work," Mr. Ellis said. "He felt that Duke dropped the ball."