Four Nepalese and one Romanian were among those killed in the bombing, which came after a series of recent Taliban suicide attacks targeting the Supreme Court, the airport, the presidency and a CIA office.
The US has been pushing for peace talks as 100,000 NATO combat troops prepare to leave Afghanistan next year and local security forces take on the fight against the Islamist extremists.
"Four Nepalese guards, one Afghan guard and two Afghan civilians have been killed," Kabul police chief Mohammad Ayoub Salangi told AFP after the attack, which started at about midnight GMT.
An AFP photographer saw one badly shaken guard with bloody face wounds and a bandage wrapped around his head being helped from the site outside the compound of the Dubai-based Supreme Group.
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The group provides many NATO bases with food, water, fuel and other supplies, as well as maintaining military storage buildings and accommodation and its compound is close to UN offices and a string of NATO bases.
Salangi said the attack began with a suicide bomb in a large truck, and two or three insurgents then fought guards for about 30-40 minutes. All the attackers were killed.
The Taliban claimed today's attack, as pressure grows on the Afghan government to secure a peace deal with the rebels before international troops pull out by the end of 2014.
"An important foreign logistic and supply facility was attacked, first by an explosive-filled truck which removed all the barriers and followed by devoted mujahideen armed with small and heavy weapons entering the base," the Taliban said in a statement.