Panjshir, an ethnically Tajik area northeast of Kabul, was a bastion of anti-Taliban resistance during the extremists' 1996-2001 regime, and has been among the most peaceful provinces in Afghanistan since they were ousted.
The attack, which was claimed by Taliban insurgents in a text message sent to the media, will heighten concerns about the militants' ability to strike in districts where they have little presence or public support.
"Six suicide bombers wearing police uniform entered the governor's office. Our security team responded and all, except one who detonated himself, were brought down," Abdul Kabir Waseq, the governor's spokesman, told AFP.
Waseq said that an explosives-packed car that had not been detonated was also recovered from the scene.
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The Afghan government immediately hailed the security forces for their actions, with the interior ministry spokesman saying that they were "more capable than ever".
The attack came after a major assault on Kabul on Friday, when the Taliban launched a suicide and gun strike on an international compound in the city centre, triggering a battle that lasted several hours.
All four militants, one policeman and two civilians died in that attack.
The police, army and special forces are being trained up by the international coalition, but there are widespread fears that they will not be able to impose security after 12 years of war.
In Baghlan province, which neighbours on Panjshir, a suicide bomber struck outside government buildings 10 days ago, killing 14 people including a local politician.
The insurgents launched their annual "spring offensive" last month vowing to use suicide blasts to inflict maximum casualties and warning Afghans working for President Hamid Karzai's regime to distance themselves from the government.