"The brutal police chief of Kandahar has been killed along several other officials", a Taliban statement said.
The deceased have been identified as provincial police chief Abdul Razik, Kandahar intelligence chief Abdul Mohmin and province governor Zalmay Wesa, Kandahar's Deputy Provincial Governor Agha Lala Dastageri said. "I express my deepest sympathy and grief with all people of Afghanistan, especially with residents of the town".
But a person with knowledge of the incident said in a telephone interview that "several sources" reported that the three were killed.
Miller survived the attack.
At least two other Afghan officials also were killed in the incident, which comes just two days before key elections in Afghanistan.
Raziq had been police chief of Kandahar since 2011 and had been accused of severe human rights abuses, including running a secret torture center.
A total of three USA nationals were wounded Thursday after a Taliban sympathizer dressed himself as a member of the Afghan security forces and opened fire at the residence of the governor of Afghanistan's Kandahar province.
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"When the Taliban are determined to kill me, my soldiers and my people, I cannot be gentle on them, and I can never forgive them", he said.
"The representatives of the Islamic Emirate identified presence of foreign forces as the greatest obstacle obstructing true peace and solving problems, adding that Afghanistan is an Islamic country and has its own Islamic values and culture".
The attack, which the Taliban claimed responsibility for, in the district of Bagram in Parwan province, also wounded three Afghan civilians. He was also highly respected by US officers who saw his ruthless methods as the most effective weapon against the Taliban.
After the attack, the city was "full of military forces" as per a witness.
Gen. Scott Miller, the commander of USA and North Atlantic Treaty Organisation troops in Afghanistan, who was present at Thursday's meeting, was unhurt in the incident. Some 2,500 candidates are competing for 249 seats in the lower house.
On Wednesday, an Afghan Parliament member, Abdul Jabar Qahraman, who was seeking re-election, was killed in a Taliban bomb blast in neighboring Helmand province.
Coming before nationwide parliamentary elections Saturday, the loss of the Kandahar leadership casts a further shadow on a political season already marred by bloodshed.
It also is seen as a key milestone ahead of a United Nations meeting in Geneva in November, where Afghanistan will be under pressure to show progress on "democratic processes".