Quick-response commando teams rushed to hunt down the attackers, who unleashed rockets and gunfire from a nearby building.
"I can confirm an attack at the IEC (Independent Election Commission) headquarters," IEC spokesman Noor Mohammad Noor told AFP.
"We heard two explosions inside the IEC compound, the sound of firing is still ongoing, but people are safe and are in (reinforced) safe rooms."
A Taliban spokesman said via a recognised Twitter account that the insurgent group was behind the attack.
On Tuesday, Taliban suicide attackers stormed a separate IEC office in Kabul, killing five people.
The Taliban have vowed a campaign of violence to disrupt the elections on April 5, urging their fighters to attack polling staff, voters and security forces in the run-up to election day.
Interior ministry spokesman Sediq Sediqqi said: "Initial information shows that three or four attackers have occupied a building and are firing on the IEC office."
The venue had been due to hold a press conference shortly after the attack to announce details on security preparations for the election.
But there are fears of a repeat of the bloodshed that marred the 2004 and 2009 elections, when the Taliban displayed their opposition to the US-backed polls through violence.
Another bloody election would damage claims by international donors that the expensive intervention in Afghanistan has made progress in establishing a functioning state.
Some Kabul restaurants and shops popular with foreigners have closed for the election period due to the risk of attack.
Today's assault came the day after Taliban attackers raided a Kabul guesthouse used by a US anti-landmine charity, killing two people.
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