Miller was not hurt in the assault claimed by the militant group that also wounded at least 12 people, including three Americans and a provincial governor, in the southern city of Kandahar on Thursday.
Dastageri said provincial intelligence chief Abdul Mohmin also died inside the governor's sprawling residence where the attack occurred.
Sources told TOLOnews that the bodyguards of Kandahar governor, Zalmay Wesa, were involved in the shooting.
The Americans were wounded in the cross-fire after gunfire erupted at the palace, Peters said.
But a person with knowledge of the incident said in a telephone interview that "several sources" reported that the three were killed.
General Scott Miller, the top U.S. commander in Afghanistan who had been at the meeting with Raziq only moments earlier, was uninjured in the attack, but the local commander of the NDS intelligence service was killed and the provincial governor was severely wounded.
Taliban spokesman Qari Yousuf Ahmadi said the militant group carried out the attack, and Miller was the target.
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Butler later tweeted a message from General Miller, saying "Today I lost a great friend Lt. Gen. Raziq".
The controversial Kandahar police chief, described by Human Rights Watch a year ago as the southern province's "torturer in chief", had risen through the ranks to become one of the most powerful security heads in Afghanistan.
Two American troops were also wounded in the shooting. "Responding to the shooting, Pentagon spokesman Lieutenant Colonel Kone Faulkner told Reuters that the attack will not change the United States resolve in its South Asia strategy if anything it made them more resolute".
A bomb placed under a sofa killed an Afghan election candidate on Wednesday, officials said, as deadly violence escalates ahead of the October 20 parliamentary ballot. The Taliban say they were targeting Gen. Miller. A veteran of some of the U.S. military's most secretive combat units, he formerly served as commander of the U.S. Joint Special Operations Command and participated in numerous combat operations, including in Mogadishu, Somalia, in 1993 and the wars in Afghanistan and Iraq since 2001.
"Over 70,000 security forces are there to maintain security". Seen as a close USA ally and a fervent enemy of the Taliban, Raziq was also deeply controversial.
Another major attack previous year inside the Kandahar governor's office took a heavy toll on officials, killing a deputy governor, the ambassador of the United Arab Emirates, and members of Parliament.
The Taliban quickly claimed responsibility for the attack, which takes the number of candidates killed so far during the campaign season to at least 10.