Militants with guns and rocket-propelled grenades attacked the governor's office, and ten explosions including six suicide blasts rocked the city, the heartland of the Taliban, after violence began around 1:00 pm.
Gunmen occupied a hotel near the local office of Afghanistan's intelligence service, while suicide bombers tried to attack two police offices but were shot before they could reach their targets.
In chaotic scenes, an AFP reporter said gunfire was still ringing out as ambulances evacuated the wounded, who included five policemen, from the area.
"Small-arms fire is still going on. Two RPGs (rocket-propelled grenades) have been fired onto the (governor's) building so far," provincial spokesman Zalmay Ayubi told AFP.
"The northern and eastern sides of the compound are under direct attack," he said, also giving details of the other attacks.
It is believed that Kandahar governor Tooryalai Wesa was holed up in his compound.
A spokesman for Kandahar's main hospital, Doctor Hashem, said that 30 people had been brought in with injuries, including five police.
The Taliban claimed responsibility for the attacks, with spokesman Yusuf Ahmadi claiming that "heavy casualties have been inflicted on the enemy".
The militia had warned on Friday that this week's killing of al Qaeda leader Osama bin Laden by US forces in Pakistan would give "a new impetus" to their fight against foreign and Afghan forces.
But Ahmadi said the Kandahar attacks were planned for nearly three weeks and were part of the start of the Taliban's annual spring offensive announced last week. He claimed they could last for hours and warned locals to stay indoors.
The assault against the heavily guarded governor's compound was launched from two nearby buildings including a shopping mall which the attackers had ordered shopkeepers to leave shortly before the violence began.
There are around 130,000 international troops in Afghanistan, two-thirds of them from the United States, battling the Taliban and other insurgents.
Limited withdrawals from seven relatively peaceful areas, only one of which is in southern Afghanistan, are due to start in July ahead of the planned end of foreign combat operations in 2014.
International forces claim that Kandahar and the surrounding area are now safer following months of intense fighting to clear traditional Taliban strongholds.
But government officials and other targets are still frequently targeted by militants in the city, the biggest in Afghanistan's south.
Nearly 500 Taliban prisoners escaped from Kandahar's prison last month through a huge tunnel in a major embarrassment for the authorities.
Also in April, Kandahar's police chief was killed by an attacker in a police uniform, while in January Wesa's deputy was killed.
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