In a separate attack that went unclaimed, a roadside bombing in eastern Ghazni province killed at least three police officers, including a district police chief.
A Taliban suicide bomber has detonated an explosive-packed military vehicle on the approach to the provincial governor's residence and police headquarters in the Afghan province of Kandahar.
At least three people were killed in Wednesday's blast in Kandahar's Sha Wali Kot district.
Bloodshed is escalating anew in Afghanistan even as the United States tries to broker a peace deal between the Taliban and Afghan government after almost two decades of war.
"At around 4 am [2330 GMT], a suicide bomber driving a large [Afghan security force] truck came under fire from security forces before reaching his goal, but detonated explosives near police headquarters and the governor's residential complex," the governor's spokesman said.
The three dead were members of the security forces while the 14 people wounded included civilians, he said, adding the police headquarters and governor's compound suffered severe damage.
The Taliban claimed responsibility, saying in a statement that the police headquarters had been used as a military hub for security force operations against the insurgents.
Attack in Ghazni
Diplomats say the resurgence of attacks is heightening mistrust just as the Afghan government and Taliban are set to enter peace negotiations and as the United States withdraws forces under a deal with the Taliban struck in February.
In the roadside bombing in Ghazni, Wahidullah Jamazada, the provincial governor's spokesman, said Habibullah, the police chief of Dayak district, was killed along with his two bodyguards.
Habibullah, who like many Afghans uses only one name, was inspecting checkpoints early in the morning when the attack happened, Jamazada said.
Separately, the defence ministry said Afghan soldiers repelled Taliban attacks on Tuesday on army checkpoints in the district of Khogyani in eastern Nangarhar province. The statement said at least 20 Taliban insurgents were killed, including their group leader.
The Taliban did not claim responsibility for the Nangarhar attack or issue any statements about it. Both the Taliban and Daesh are active in eastern Afghanistan, especially in Nangarhar.
An explosion in Kabul on Tuesday injured two civilians and security forces said they had thwarted large attacks in and around the capital.
Taliban, government trade blame
The Taliban and the Afghan forces have been trading blame over the recent surge in attacks across the country — even as peace efforts press on to try and bring about the start of direct peace talks between the Afghan government and the Taliban.
The Taliban accuse government forces of targeting them in their homes, their families bearing the brunt of those anti-Taliban operations. Kabul, meanwhile, accuses the Taliban of stepping up attacks against both civilians and the security forces.
The violence has been a key obstacle to any negotiations between the Taliban and the Kabul government — talks that were envisaged by the US-Taliban deal signed in late February to end 19 years of war in Afghanistan.
The deal also called for the Afghan government to free 5,000 Taliban prisoners in exchange for the Taliban releasing 1,000 government and military personnel they hold captive. So far, the government has freed 4,015 imprisoned insurgents while the Taliban have freed 669, according to data by the Afghan government.