At least three attackers raided an unoccupied nearby building and targeted the election offices in a stand-off that continued for more than four hours as elite Afghan commandos tried to hunt them down.
"Police have surrounded the building, but the fighting isn't over yet," Kabul police spokesman Hashmat Stanikzai told AFP, adding there were no details on casualties.
Independent Election Commission (IEC) spokesman Noor Mohammad Noor said that staff were hiding in reinforced safe-rooms, but all employees were unharmed.
Kabul airport, which is in the same eastern area of city, was closed for some hours, with planes diverted to Karachi and returning to Delhi as well as other destinations.
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On Tuesday, Taliban suicide attackers stormed a separate IEC office in the Afghan capital, killing five people.
As tensions rise, some restaurants and shops popular with foreigners have shut for the election period due to the risk of attack.
The militant group has vowed to disrupt the vote on April 5, urging their fighters to attack polling staff, voters and security forces in the run-up to polling day.
Interior ministry spokesman Sediq Sediqqi said three or four attackers were involved in the attack on the office, where a press conference had been scheduled to announce details on security preparations for the election.
The vote to choose a successor to President Hamid Karzai, barred constitutionally from seeking a third term, will be Afghanistan's first-ever democratic handover of power.
But a repeat of the bloodshed that marred the 2004 and 2009 elections would damage claims by international donors that the expensive 13-year US-led intervention has made progress in establishing a functioning Afghan state.