The minibus was crossing a bridge 20 km (12 miles) south of the city on Friday when the attack took place.
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We have arrested eight suspects so far. The investigation is going on
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General Akram Khakrezwal
However, officials believe the number of people killed in the incident is lower than their original estimates.
They now say eight or nine people died as the bus was attacked with, what the authorities believe was an anti-tank mine rigged to a mortar bomb.
The head of security in Kandahar, General Akram Khakrezwal, said: "We have arrested eight suspects so far. The investigation is going on."
Fierce fighting
Mr Khakrezwal said the authorities believe the Hezb-e-Islami faction of warlord Gulbuddin Hekmatyar, along with some Taleban remnants, are responsible for the attack.
US-led forces have recently been involved in what they described as the fiercest fighting for months in a mountainous region east of Kandahar.
Up to 18 anti-government fighters were said to have been killed in the clashes near Spin Boldak which began on Monday.
Kandahar police chief Ustad Nazar Jan said according to the driver of the minibus, who survived, eight passengers had died.
"We are still trying to find the exact figure," he added.
Continuing efforts
Mr Jan said the driver had said 12 passengers were on board, all from nearby villages.
US military spokesman Colonel Roger King Colonel King said efforts to clear the area - dubbed Operation Mongoose - were continuing.
Also on Friday, the US army confirmed that four American soldiers had been killed on Thursday when a military helicopter crashed near the capital, Kabul.
The Black Hawk helicopter crashed near Bagram air base on a routine training mission in what appeared to be an accident.
Kandahar - near the border with Pakistan - is a former stronghold of the Taleban.
Many Taleban and al-Qaeda suspects fled into Pakistan following US attacks in 2001.
Up to 8,000 US troops are stationed in Afghanistan.