The political dispute within the Washington-backed government deepened on Sunday when another governor and ally of Mr. Noor in the north, Abdul Karim Khadam, refused an order from Mr. Ghani that he resign as governor of Samangan Province.

“The government’s decision is unjust and unfair,” Mr. Khadam said in a telephone interview, adding that it goes against a power-sharing agreement reached last spring between the Jamiat party and the president.

Mr. Khadam took pains to emphasize that his refusal to obey the order did not amount to an armed rebellion. “Our opposition to the government does not mean we are rebelling,” he said.

Still, the growing standoff spells trouble for the Kabul government. Mr. Noor’s media office said in a statement that he supported the defiance of another governor, and criticized the president.

“Ghani’s recent moves are alarming, and we hope he soon wakes up to the realities on the ground, or else he is taking the country to the edge of collapse,” it said.

In defying the central government, Mr. Noor has aligned himself with ethnic minorities in the north, including the Uzbek warlord Abdul Rashid Dostum, who went into exile in Turkey to avoid possible prosecution over accusations he had ordered his bodyguards to detain and rape a political rival. Mr. Dostum retains the title of vice president.

Mr. Ghani appointed as the new leader of Samangan an associate of a onetime insurgent leader and Taliban ally, Gulbuddin Hekmatyar, who reconciled with the government last year. Officials in Mr. Hekmatyar’s party have accused Mr. Noor of receiving backing from Russia, which they say is trying to carve out an area of influence in northern Afghanistan.