North Atlantic Treaty Organisation spokesman Colonel Knut Peters said Miller, who took command of USA and forces and the NATO-led Resolute Support mission in Afghanistan last month, was uninjured but two Americans were wounded in the crossfire.
"The shooting happened as they were leaving the meeting", the official said, adding two members of Afghanistan's spy agency also were injured.
Security forces swarmed the city after the attack at the provincial governor's office where the senior Afghan and foreign officials had gathered, witnesses told AFP. At the time, he said a nationwide campaign against the Taliban was needed and that he believed the group "was puppets of other countries".
The attack took place on Thursday afternoon after Miller's meeting with Kandahar's governor and provincial police chief, Geneneral Abdul Raziq, which took place at the governor's office. Two Americans were injured in the incident at the compound, a North Atlantic Treaty Organisation spokesperson said, and a local cameraman was reportedly killed.
Three Americans, including a soldier, civilian and contractor, were wounded in the cross-fire and had been evacuated from the scene.
Afghan and worldwide security officials said Gen Raziq had been shot in the back as he left the meeting and died from his wounds. "We are being told the area is secure".
The Taliban claimed responsibility for the attack, saying they had targeted both Miller and Raziq, who had a fearsome reputation as a ruthless opponent of the insurgents.
He had survived a number of assassination attempts, including suicide attacks, but had managed to strengthen security in Kandahar, the birthplace of the Taliban militants. Ahmadi asserted that Miller had been killed, a claim denied by US military officials. "Initial reports also say the attacker is dead". He had been credited with security improvements in recent years. His forces received Western training and funds, and US military officials often consulted him.
The attack was a devastating blow to the Afghan government ahead of parliamentary elections on Saturday, which the Taliban have vowed to disrupt.
Earlier Wednesday, a parliamentary candidate in southern Helmand province was killed when a bomb exploded while he was holding a meeting in the courtyard of his campaign headquarters in the provincial capital, Lashkar Gah.