The US, meanwhile, confirmed strikes against the insurgents in Helmand province with "more than 50 casualties".
Afghan security forces patrol, after recapturing control of the city from Taliban militants, in Farah.
The tactics used in the attack "track with" the tactics that the Haqqani faction has used in the past, he said and added: "We at this time do not believe it was an ISIS attack".
In a later tweet, he said there were concerns that an attacker in a US military uniform was on the base and that head counts were underway.
Danish said 10 attackers were involved; three with suicide vests and seven others armed with weapons and wearing military style uniforms.
There was no breach of the North Atlantic Treaty Organisation compound, said Lt. Col. Martin O'Donnell, a spokesman for the coalition in Kabul.
The Taliban also claimed responsibility for a predawn attack on a police station in the capital of Logar province, about 70 kilometers (45 miles) southeast of Kabul.
Last month, two explosions in Kabul killed at least 26 people, including nine journalists who had arrived to report on an initial blast and were targeted by a suicide bomber which was claimed by the Islamic State fighters. A suicide auto bomb was set off at the gates before three gunmen in suicide vests stormed the compound.
Mohammad Salim Roodi says the attack took place in Girishk district when the police tried to stop a suspicious vehicle outside the governor's compound. Among the wounded were two children, the media reported.
The Taliban claimed the attack.
Another early morning attack struck the capital of Kandahar province, when a suicide vehicle bomb blast killed three civilians and wounded 13 others, a provincial official told reporters.
But the Taliban have always insisted on talking only to the U.S., whom they consider the main party to the conflict, in any initial talks.
Image copyright EPA Image caption Cleaning up in Kabul - the capital keeps getting hit by attacks Who are the Taliban?
They were captured for different reasons ranging from cooperating with Afghan security forces to being a member of the local police force, Saleem said.
Elsewhere in Afghanistan, the Taliban attacked a district headquarters in the northern Takhar province, killing five security forces, according to provincial police spokesman Khalil Asir.