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 informed after the attack, which started at about 4:30am (midnight GMT).
A Romanian male civilian contractor was also killed and another wounded in the attack, Adrian Kozjacski, the head of the Romanian diplomatic mission in Afghanistan told AFP.
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.
The group provides many NATO bases with food, water, fuel and other supplies, as well as maintaining military storage buildings and accommodation.
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 bomb left a large crater in the ground, and reduced walls and a guard post to a pile of rubble and twisted steel. Police said some suicide vests were later detonated by security forces.
The Taliban claimed Tuesday'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.
A Taliban office that opened in the Gulf state of Qatar on June 18 to start peace talks enraged President Hamid Karzai by styling itself as an unofficial embassy for a government-in-exile.
Karzai broke off bilateral security talks with the Americans and threatened to boycott any peace process altogether.
The Taliban, who have been fighting a guerrilla war for 12 years, have consistently refused to hold any peace talks with the Afghan government, with rebel leaders labelling Karzai as a US puppet.
But the Pentagon on Monday expressed optimism over negotiations for a US-Afghan security deal which would allow a "residual" US force to stay in the country with legal immunity.
NATO commanders, the Afghan government and the Taliban have all vowed to fight on at the same time as international efforts are made to secure a ceasefire and kickstart a peace process.
Only hours after the Qatar office opened, a Taliban rocket attack killed four Americans on the largest military base in Afghanistan.
Days later, a suicide squad targeted the presidential palace and a CIA office in Kabul.
US President Barack Obama has said he anticipated "a lot of bumps in the road" but that a peace settlement with the Taliban was the only way to end violence in Afghanistan.
More than 3,300 coalition personnel have been killed in the country since 2001, peaking at 711 deaths in 2010, according to the independent icasualties.org website.
Half of the 68,000 US troops in Afghanistan will exit by February, and the newly-trained Afghan army and police are increasingly taking the lead in the battle to suppress the Taliban.
The Taliban were deposed in a 2001 US-led invasion for sheltering Osama bin Laden and other al Qaeda leaders after the 9/11 attacks on New York and Washington.