Kabul, Afghanistan (CNN) -- Explosions and heavy automatic gunfire were heard hours after five well-armed suicide bombers attacked the British Council in the Afghan capital Friday, leaving at least eight people dead, officials said.
White smoke billowed from a building in the compound while heavily armed British and Afghan forces cordoned off the area in the center of the capital, establishing a security perimeter around the buildings.
The attacks occurred inside a well-guarded Kabul neighborhood, leaving at least 16 people wounded, the Afghan Interior Ministry said.
Among the dead was one New Zealand Special Forces service member, officials said.
"I have limited details about the soldier's death, but I am advised that he died during fighting that followed an attack by insurgents in Kabul in the last few hours," New Zealand Prime Minister John Key said.
"On behalf of the government, I want to offer my condolences to the family of the soldier."
The strike, which the Taliban have claimed responsibility for, coincides with the 92nd anniversary of Afghan independence from Great Britain.
In the first attack, a militant drove a vehicle packed with explosives toward the Council's main security gate before detonating the device, according to Afghan police spokesman Hashamap Stanikzai.
A second man then attempted to enter the compound wearing a vest filled with explosives. He also detonated himself, Stanikzai said.
Police say two militants were killed in a firefight with security forces. The other three detonated their explosives.
Gunfire could be heard throughout the incident, and military helicopters circled overhead.
The British Council is a British government-affiliated body that fosters cultural and academic exchanges in Afghanistan.
Afghan President Hamid Karzai condemned the attack, as did the NATO-led International Security Assistance Force in Afghanistan.
"Initial reports indicate a combination of multiple vehicle-borne and personal-borne (improvised explosive devices) were detonated," the ISAF statement said.
NATO commander Gen. John Allen pledged to hold "the perpetrators accountable for their actions."
Meanwhile, an embassy spokesman said British government personnel are coordinating with Afghan authorities to secure the area.
The strike occurred not far from the Intercontinental Hotel, the scene of another insurgent attack against a high-profile Western target in June.
CNN's Matiullah Mati contributed to this report.