Police vehicles and weapons were also seized by the attackers, Khan said.
He laid the blame for the raid on the "enemies of Afghanistan".
String of attacks
The ambush was the latest in a string of attacks on police.
Eight police were killed on Saturday - four while destroying opium poppies in Kandahar and four manning a checkpoint in Helmand province.
On April 7, seven police in a poppy-eradication team were killed in Kandahar.
The attacks come despite about $4bn the US has spent to train and equip police the last three years.
Also on Monday, the British ministry of defence said in a statement that two servicemen from the RAF Regiment had died in a roadside blast in southern Afghanistan.
Two other servicemen were hurt, but their injuries were described as not life-threatening.
Routine patrol
The British servicemen were carrying out a routine patrol about west of Kandahar airfield at 6.48pm local time on Sunday when their vehicle drove over the explosive device.
"Medical care was given at the scene and all four servicemen were evacuated to the field hospital at Kandahar airfield," the UK defence ministry statement said.
Kandahar province was where the Taliban rose to prominence in the early 1990s and is one of the worst hit regions in anti-government campaign led by the group since their removal from power.