Ismatullah Alizai, Kandahar's police chief, the first blast struck the vehicle of a private security company, killing four of the guards.
The interior ministry later identified the firm as US Protection and Investigation (USPI) company. It gave the same death toll.
Texas-based USPI is one of the biggest security firms working in Afghanistan.
About half an hour later, as police and reporters gathered at the site, a second bomb exploded just metres away.
"It took place as the security chief with his investigation team arrived at the site," the ministry said.
"The explosion killed three, including a police officer and two policemen."
A policeman at the scene, Mohammad Jan, said four officers were wounded including the security chief, who is also the deputy provincial police chief, Abdul Hakim Angar.
A news reporter was also slightly wounded.
Both bombs were remotely detonated, the interior ministry said in a statement.
Qari Yousef Ahmadi, a purported Taliban spokesman, said on Thursday that the co-ordinated bombings were planned to hit police responding to the first blast.
|Police officers gather at the site of Thursday's|
blasts in the centre of Kandahar city [AFP]
The violence in Kandahar came less than a week after Mullah Dadullah, the Taliban field commander, was killed during a US-led operation in neighbouring Helmand province.
The Taliban have warned of "bad consequences" if the government didn't hand over Dadullah's body to his relaives.
Kandahar's governor has said that Dadullah was buried at a secret location near Kandahar.
In another attack on Thursday, a remote controlled bomb struck a vehicle of the provincial police chief of the northern province of Badakhshan, killing a guard and wounding the officer and his aide, the interior ministry said.
A provincial official, Shamsul Rahman, blamed the attack on the "opposition forces."
Also early on Thursday, Pakistani and Afghan troops exchanged mortar and gun fire on their disputed border, days after clashes on the frontier claimed more than a dozen lives, a Pakistani official said.
The two-hour battle erupted after Afghan forces fired a mortar at Pakistani soldiers near the Teri Mangal area in the Khyber tribal district, a Pakistani military spokesman said on condition of anonymity.
"Pakistani forces responded effectively and the exchange of fire continued until 5am local time. There were no casualties on the Pakistani side," the spokesman said.
There was no immediate response from Afghan authorities.
The clash happened near an area where a US soldier and a Pakistani trooper were shot dead on Monday after a meeting, also involving Afghan officials, that was aimed at calming tensions.
Afghan officials meanwhile accused Pakistan of starting clashes in the same area on Sunday that continued into Monday, saying Pakistani troops pushed 4km over the disputed border.
Pakistan denied the charges.
Thirteen Afghans were killed in the fighting, which included rocket fire, Afghan officials said.