The attacks have driven home that the Taliban have no intention of ending the violence, even though they have indicated they are willing to talk peace and have opened an office in Qatar for that purpose.
"This (attack) has no link to the peace process," Taliban spokesman Zabiullah Mujahid told The Associated Press in a telephone call. Attacks "will continue all over the country occupied by the foreigners," he said.
Before dawn, a suicide bomber drove a small truck packed with explosives to the outer gate of the logistics center used to supply NATO troops and detonated it, said Kabul provincial police chief Mohammad Ayoub Salangi. The explosion blasted a huge crater in the ground and damaged a guard tower.
Two truck drivers waiting to enter the compound were killed in the blast along with the bomber, he said.
Then four gunmen stormed into the breach and battled with security guards. An Afghan police special response team and security guards battled the attackers for about an hour before killing them, the Interior Ministry said in a statement. One Afghan and four Nepalese guards were also killed, the ministry said.
In a statement on the Taliban website, Mujahid said only three militants were involved in the "attack on a big foreign base important for NATO logistics," listing the assailants by name.
The Taliban opened a political office in Doha last month, indicating they were prepared to enter into Afghan peace talks, but they did not renounce violence.
Evidence of this erupted the following week. Taliban suicide attackers got past preliminary security checks and opened fire on guards at a gate to the presidential palace in the heart of Kabul.
Before that in June, heavily armed fighters launched a failed assault on NATO's operational headquarters at Kabul's international airport and detonated a car bomb outside Afghanistan's Supreme Court.
The U.N. deputy chief, Jan Eliasson, who was in Kabul wrapping up a five-day trip to Afghanistan when Tuesday's attack hit, 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."
The Taliban have refused to negotiate with President Hamid Karzai's government in the past, saying the U.S. holds effective control in Afghanistan, but the Americans are hoping to bring the two sides together. Long-stalled negotiations have become more urgent with Afghan presidential elections and the withdrawal of most U.S. and other foreign combat troops looming in 2014.
The possibility of peace talks got off to a rocky start, however, after the Taliban opened the Doha office under the name "Islamic Emirate of Afghanistan" and the flag it used while ruling Afghanistan. Karzai and other Afghans reacted sharply to the move, saying that agreements had been violated and that the office was more akin to a rival embassy than a bureau for peace negotiations.
The Taliban have since been forced to remove the offending flag and sign, but talks have yet to begin.
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, hoping for direct contacts between the parties. "As long as those contacts continue, there's no specific need for the United Nations to be involved."
Also Tuesday, in the eastern province of Paktika, local police commander Azizullah Karwan said six Taliban militants were killed in a clash with one of his patrols.
He said there were no police casualties.
In Ghazni, the neighboring province to the west, three policemen were killed and three wounded in a gunbattle with the Taliban around midday, district police chief Kasim Desiwal said. Four Taliban fighters were killed, he said.
Associated Press writer David Rising contributed to this report.