Al Jazeera's James Bays, reporting from Kabul, said it was an "audacious and very well-planned attack".
"The Taliban are telling Al Jazeera that six of their men were sent to stage this attack ... wearing suicide vests and carrying AK 47s.
"There are two things significant about this; Logar is the province right next to Kabul, and the second thing is that in the governor's compound is the office of the Independent Election Commission (IEC).
"It is going to worry them [the commission] a lot. It is a huge security challenge. Logar is a place that has had a lot of violence."
The attack came as a United Nations report said security fears in many parts of Afghanistan were hindering preparations for the presidential election to be held on August 20.
The report, compiled by the UN mission in Afghanistan and Afghanistan's independent human rights commission (AIHRC), said insecurity had "severely limited freedom of movement and constrained freedom of expression for candidates".
"Our position is that where there is no security, where the election commission can't go, I don't think we would be able to do anything"
Zekria Barakzai, deputy chief electoral officer
It said the ability of candidates and their supporters to campaign had been hampered as they are unable to attend public gatherings or visit constituents.
"These restrictions have ... created significant limitations on freedom of association and peaceful assembly, and amplified women's difficulties in participating in the electoral process," the report said.
"The same limitations have posed challenges to the complaints process and preparations for polling and counting, including voter and civic education."
Hamid Karzai, the Afghan president, on Monday outlined his manifesto for his term of office if he is re-elected, saying he would open dialogue with the Taliban.
He promised talks with them through a Loya Jirga - a traditional assembly of Afghan elders and tribal chiefs.
"If I win the election, I will summon a national Loya Jirga from across Afghanistan and ... will send invitations to our Taliban and Hezb-i-Islami brothers to come and participate in the Loya Jirga with their countrymen and find the ways for peace and security and put an end to foreign' influence."
US and Nato-led forces in Afghanistan have stepped up operations for the election, the second since the Taliban were forced from power in 2001, but fears remain that polling will be marred by violence.
Bays said: "Security officials tell us off the record they have considerable worries about what is going to happen on election day and afterwards."
General Stanley McChrystal, the commander of US and Nato troops in Afghanistan, said in an interview published on Monday that Taliban fighters were advancing out of their traditional strongholds in Afghanistan's south and east.
"It's a very aggressive enemy right now," he told The Wall Street Journal newspaper.
"We've got to stop their momentum, stop their initiative. It's hard work."
|Some candidates have complained about the level of security they have received [AFP]
Some candidates in the presidential election have complained they have not been provided with sufficient security.
One campaign manager for a presidential candidate was quoted by the report as saying that security considerations had played a role in deciding to shift from large rallies to smaller ones.
"Provincial council candidates in provinces such as Khost, Kunduz, Logar, and Kandahar reported that insecurity hampers their ability to campaign in many districts," the report said.
Al Jazeera's Hashem Ahelbarra, reporting from Kabul, said: "The [Afghan] army is so stretched thin to the point that they have told some candidates 'we don't have enough people to provide security for you and therefore you have to use your own people for security'."
In some areas there have been no campaign rallies and concerns remain that voting may not be possible in some parts of the country.
A final list of areas where voting will be able to take place is expected to be published on August 15.