A gun battle ensued between the security forces as the assailants vied for control of the building, said spokesman Khaled Omar.
The victims included three employees of the commission and four members of local security forces, he said.
"I saw two suicide bombers myself," he revealed, adding that he had seen bombers' body parts strewn on the ground.
"A suicide bomber blew up himself inside the commission and the others set a part of the building on fire."
"We (the staff) are out of the building now while the security people deal with the incident."
Pictures posted on social media showed thick black smoke billowing from the commission's offices, in the Ghout al-Shaal district west of central Tripoli.
There was no immediate claim of responsibility for the attack.
The electoral commission has been registering voters ahead of new elections, expected for later this year.
Libya has been in a state of turmoil since a 2011 conflict resulted in the overthrow of longstanding ruler Mmammar Gaddafi.
Extremists including some with links to ISIS and al-Qaeda have a presence in Libya. Libyan and Western officials say they are concentrated in remote desert areas, but also have sleeper cells in coastal cities.
The Quartet on Libya expressed on Monday its support for holding presidential and parliamentary elections this year.
Meeting in Cairo, the European Union, the African Union, the Arab League and the United Nations said they will provide observers and electoral assistance to ensure the voting is free and fair.
The group also emphasized the need for Libya to have a unified army under civilian command, a goal that has proved elusive under the current proliferation of militias.
