In addition to Kandahar police chief Gen. Abdul Raziq's death, the local leader of the country's main intelligence agency and a journalist were killed, Datyagiri said.
The Taliban spokesman Qari Yousuf Ahmadi in a statement claimed that the candidate has been killed along with his three colleagues in the tactical explosion.
US forces confirmed the attack, casting it as "Afghan on Afghan" violence.
There were conflicting reports on the fate of Wessa and Abdul Momin, with Afghan news media reporting variously that they had been wounded or killed. North Atlantic Treaty Organisation spokeswoman Debra Richardson said three service members were wounded in the bombing but didn't provide more details.
"It is a big loss for Afghanistan", Shakeba Hashimi, a legislator from Kandahar, said by cellphone as she was en route to his funeral at a hospital there. "He was seen as crucial to the security of Kandahar, the birthplace of the Taliban where the group continued to have a presence". But he was also accused of torture and corruption.
Three senior Afghan officials were reported to be among the casualties, but there were conflicting accounts on whether they were killed or wounded.
"This serious attack seems likely to shake the confidence of the government as security forces prepare for one of their largest operations of the year, guarding more than 5000 polling centres in the upcoming parliamentary elections", said Graeme Smith, a consultant for the conflict monitoring organisation International Crisis Group.
Another witness said the city was "full of military forces".
Miller assumed command last month from Gen. John Nicholson and was still carrying out initial assessments of the security situation in Afghanistan.
Raziq is often characterized as a USA -backed warlord in Afghanistan.
Afghanistan is tense ahead of the October 20 legislative election after the Taliban pledged to attack the ballot. The Taliban has threatened to disrupt the voting and has warned Afghans against participating in what the radical Islamist group regards as a pretext for perpetuating US intervention in the country.
Jabar Qahraman, an election candidate in the southern province in Afghanistan, was killed in his campaign office on Wednesday after explosives kept under his sofa blew up.
The flamboyant commander, he had survived several attempts on his life over many years and narrowly escaped an attack last year in which five diplomats from the United Arab Emirates were killed in Kandahar.