Powerful explosions followed by bursts of gunfire were heard in the provincial capital, Charikar, which is only an hours drive north of Kabul.
The governor, Abdul Basir Salangi, said that up to six suicide bombers had struck in the attack that lasted at least an hour.
The Taliban have been quick to claim responsibility for the attack, which was launched at 1100 hours on Sunday.
A suicide car bomb was detonated, after which five other militants wearing bomb vests broke into the compound, police said.
Mr Salangi told the BBC, “A suicide attacker wearing a police uniform… detonated his explosives outside the northern gate. Then five others attacked my office.”
“They managed to get inside the compound to the halls. The fighting went on for one hour.”
A police source said, “They even got close to the governor’s office… but his bodyguards opened fire, killing the last attacker, who was using a rocket-propelled grenade.”
A meeting of security chiefs was under way when Sunday’s attack occurred.
Local police and intelligence chiefs were present, along with advisers from the international coalition.
This all seems to be part of a Taliban strategy to assassinate important officials close to the Afghan government. The softer targets are easier for them than taking on the US lead military head-on.
Rising up the ranks in Afghan local government used to be a good get rich quick scheme. Now, holding office is a bit of a death wish for ambitious politicians.
The Taliban really are A-Grade dickheads. But we have to concede they are certainly focussed on getting what they want.