The morning attack was the latest in a series targeting high-profile locations in the Afghan capital. The attacks have made clear the Taliban have no intention of ending the violence, even as they say they are willing to enter peace negotiations.
The U.N. deputy chief, Jan Eliasson, who was in Kabul wrapping up a five-day trip to Afghanistan when the attack took place, said continued violence could only harm the Taliban's own cause.
"I would hope that there would be steps taken by the leadership of the Taliban to realize that the tool of violence in any case cannot instill confidence in the population," he said. "There's been too much suffering there and there are too many widows, too many father-and-motherless children in Afghanistan and I think we need to instill a sense of calm."
Tuesday's attack started before dawn, when a suicide bomber drove a small truck to the outer gate of the logistics center used to supply NATO troops and detonated it. The explosion made a massive crater in the ground and damaged a guard tower, said Kabul provincial police chief Mohammad Ayuob Salangi.
Two truck drivers waiting nearby to enter the compound were also killed in the blast, along with the bomber.
Three gunmen then stormed into the breach and battled with security guards for more than an hour before being killed. Four Nepalese security guards were also killed, Salangi said.
Taliban spokesman Zabiullah Mujahid claimed responsibility for the assault, saying it was "a very effective attack that embarrassed the enemy."
Mujahid said only three militants had been involved in the "attack on a big foreign base important for NATO logistics," and listed them by name in a statement on the group's website.
The Taliban last month opened a new political office in the Gulf nation of Qatar, and indicated that they were prepared to enter into Afghan peace talks, but at the same time did not renounce violence.
The following week, Taliban suicide attackers were able to get past preliminary security checks and open fire on guards at a gate to the presidential palace in a bold attack at the heart of the Afghan government.
Earlier in June, heavily armed fighters launched a failed assault on NATO's operational headquarters at Kabul's international airport and blew up a car bomb outside Afghanistan's Supreme Court.
Eliasson said if U.N. support was needed to help start the peace process, he was glad to provide it -- but only if requested by the Afghan government.
"The reconciliation process must be, if it is to be successful, Afghan-led," he said. "What I hope will take place is, of course, contacts between the two parties ... and as long as those contacts continue, there's no specific need for the United Nations to be involved."
Take ABC13 with you!
Download our free apps for iPhone, iPad, and Android devices