Up to now, fighting involving lightly armed militias has been mainly confined to small towns and rural areas, but a group claiming to be Mandalay's new People's Defence Force said its members responded after the army raided one of its bases.
"We retaliated as one of our guerrilla base camps was invaded," said a post on the group's Facebook page from a Major Zeekwat.
The army supported by three armoured vehicles had surrounded a boarding school in Mandalay where the militia had a base, the Khit Thit news service reported.
A spokesman for the junta did not answer calls seeking comment.
The army has responded with artillery and air strikes in other places after militia groups launched attacks on soldiers, with casualties on both sides and tens of thousands of people displaced from their homes.
The United Nations General Assembly on Friday called for a stop to the flow of arms to Myanmar and urged the military to respect the results of a November election and release political detainees, including Suu Kyi.
On Saturday, Myanmar's foreign ministry released a statement rejecting the UN resolution, which it said was "based on one-sided sweeping allegations and false assumptions".
Security forces have killed at least 873 protesters since the coup, according to the Assistance Association for Political Prisoners activist group. The junta disputes that figure.