Afghan police arrive at the site of an attack in on Monday in Kabul, Afghanistan.

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NEW: All seven militants are dead, authorities say

Police say attackers storm a building near the airport

The Taliban say the attack is intended to target Americans in the airport

The airport is used by both civilians and military forces

Kabul, Afghanistan CNN  — 

Taliban fighters armed with guns and explosives clashed with security forces after taking over a building near the airport in the Afghan capital on Monday.

The fighting ended with all seven attackers dead, Afghan officials said.

The Taliban said the attack was intended to target Americans in Kabul International Airport, one part of which is used by military forces and another by civilians.

The assault on the five-story building, which is under construction, began with two suicide bombers blowing themselves up, said Kabul police official Hashtmat Stanikzai.

At least five attackers then stormed into the structure and exchanged fire with security forces, he said.

They were eventually killed, said Sediq Sediqqi, a spokesman for Afghan interior ministry.

The attack left two civilians, including a woman, injured – but no security personnel were hurt, Sediqqi said.

NATO’s International Security Assistance Force in Afghanistan said it was under lock down during the attack but had “no operational information” about what was happening.

Insurgents have carried out frequent attacks on security forces across Afghanistan in recent months amid a spring offensive by the Taliban.

Last month, a suicide car bombing on a coalition convoy in central Kabul killed at least 12 people, six of them American and six Afghan.

The insurgent group Hezb-e Islami claimed responsibility for that attack. The group is not under the Taliban leadership, but operates alongside them.