Ms. Douglas in Arizona, who declined to comment beyond her public statements, cast the dispute as one over support for the Common Core, accusing the governor of favoring those standards and saying “he has established a shadow faction of charter school operators and former state superintendents who support Common Core and moving funds from traditional public schools to charter schools.”

But Daniel Scarpinato, the governor’s spokesman, said Mr. Ducey does not support the Common Core and favors standards set by the state.

An adviser to the governor on education policy who was not authorized to speak publicly said Mr. Ducey recognized that with state tests based on the Common Core looming this spring, it would throw the state into chaos to dump the standards without going through a more deliberate process.

Mr. Scarpinato declined to comment on what has driven any animosity between the two officials, who ran on the same Republican ticket, but said the two had a “positive relationship” on the campaign trail, and have met since the inauguration.

“Governor Ducey is disappointed Superintendent Douglas has chosen this path,” Mr. Scarpinato said. “His office will continue working every day to improve educational outcomes for every Arizona child, and he hopes she joins that conversation.”

At a tense meeting on Friday, the board voted 7 to 1 — with Ms. Douglas the sole dissenter — to restore email, telephone and office access to the staff members dismissed by the superintendent. The board‘s members are appointed by the governor.

Greg Miller, a charter school administrator, said the situation had done "damage to the board and its ability to do its job." He added: “We all want to go back to work.” Business and education leaders in the state condemned Ms. Douglas’s actions.