Afghan police and Nato-led multinational forces said they were investigating the shooting late on Wednesday.
The death of civilian in military action against pro-Taliban fighters is a sore point in Afghanistan and one touched upon by Roberts Gates, the US Defence Secretary, during a visit to Kabul on Wednesday.
Karzai said on Thursday the deaths of the official and an Afghan elder, Mohammad Gul, killed in a separate mine explosion in Uruzgan Thursday were a "great loss."
The men were close colleagues of Karzai during his resistance to the Taliban, the statement said.
The president worked against the Taliban regime from a base in Uruzgan during the 2001 invasion that eventually drove the Taliban from power.
Gul was killed with two policemen when a bomb hit their vehicle on Thursday, a police commander said.
A Taliban spokesman told journalists that his group had planted the mine.
Two more policemen were killed on Thursday when Taliban fighters attacked a police post in the town of Sharan near the eastern border with Pakistan.
"Two policemen were martyred and four others were injured after Taliban riding two motorbikes attacked their posts," deputy provincial governor Malik Tanai said.
More than 720 Afghan police have been killed in attacks since March, according to the interior ministry.
Nato's International Security Assistance Force (Isaf) said meanwhile that one of its soldiers was killed in eastern Afghanistan on Wednesday after coming under fire from insurgents.
More than 90 civilians were reported killed in a US air raid on August 22 in Afghanistan [AFP]
Another soldier died from non-combat injuries, the separate US-led coalition said.
At least 212 international soldiers have been killed in Afghanistan this year alone, most of them in pro-Taliban fighter attacks, according to an AFP tally.
Around 220 died last year.
Parts of Afghanistan have been battered by Taliban fighter attacks as the group, who were removed from government in late 2001, are leading an insurgency against the government.
Gates said during his visit that the US government was planning to send extra troops to the country next year after calls from commanders on the ground for more help.
General David McKiernan, the senior US commander in Afghanistan, said on Tuesday he needed more than 10,000 extra combat troops to fight.
There are around 60,000 international soldiers already in the country, many of them in support and not combat roles.
Gates also announced a joint probe with Afghanistan into civilian deaths in an August 22 air attack that Afghan and UN officials say killed 90 civilians, but the US military says killed five to seven, along with 30-35 fighters.