KABUL, Afghanistan (AFP) - The latest Taleban strike in Kabul killed a South African father running an education charity and his two teenage children, a family spokesman said on Sunday, as the city police chief resigned after a spate of attacks.

With the US-led NATO war against the Taleban nearing its end, the insurgents have targeted foreign guesthouses, embassy vehicles, US troops and a female member of parliament in recent weeks.

Werner Groenewald, 46, his son Jean-Pierre, 17, and daughter Rode, 15, were killed in Saturday's attack on the compound of Partnership in Academics and Development (PAD), a small California-based education group.

Werner's wife Hannelie, a doctor, was working at a hospital when the attack began, Hannelie's sister Riana du Plessis, who is acting as family spokeswoman, said.

Explosions and gunfire erupted for three hours as Afghan elite commandos battled three militants who were eventually killed.

"Their house was burned down," du Plessis said, speaking in South Africa. "Hannelie went back there this morning to try to recover some of their goods, but there was nothing to recover.

"She lost everything - her children, her husband, her cats, her dogs." Taleban spokesman Zabiullah Mujahid claimed on Twitter that the compound was that of a secret Christian missionary group.

Du Plessis and friends of the Groenewalds in Kabul said the family were strict Christian but were not missionaries.

Many international aid workers, diplomats and consultants work in Kabul, though very few are accompanied by their families.

"In the midst of this unprovoked attack, Partnership in Academics and Development remains committed to providing educational resources for Afghan citizens," the charity said in a message on its website.

A family website described how the Groenewalds moved to Kabul with their two children in 2002. It said Werner was previously a Christian pastor in Pretoria, while Hannelie is a qualified doctor who answered a call "to help the sick in Afghanistan".

Kabul police chief General Zahir Zahir stepped down on Sunday shortly after he confirmed that three South Africans and an Afghan citizen were killed in the attack.

"The attackers first shot dead the director as they entered the building," Zahir said at a press conference.

NATO troop numbers in Afghanistan peaked at 130,000 in 2010 but have fallen rapidly since then. Their combat mission ends altogether on Dec 31.

Fears are growing that the declining international presence is already fuelling the Islamist insurgency.

The mission will be replaced by a 12,500-strong force supporting the Afghan army and police, who have taken over responsibility for thwarting the Taleban.

In Saturday's attack a neighbouring building was engulfed in flames as security forces hunted down the militants, at least one of whom detonated a suicide vest.

On Thursday the Taleban struck at a foreign guesthouse, wounding a guard, and a suicide bomber targeted a British embassy vehicle in a blast that killed six people.

Kabul has been hit by at least nine attacks in the last two weeks.

President Ashraf Ghani on Sunday described the Taleban as "a small minority who want to hijack the nation".

"We won't allow that," he vowed.

Militants in the southern province of Helmand in the past week also got inside Camp Bastion, a major NATO base handed over only last month.

At least five Afghan soldiers died in the fighting before order was restored on Saturday, Ghulam Farooq Parwani, a senior Afghan army commander at the camp, said.

Ghani, who came to power in September, has vowed to bring peace to Afghanistan after decades of conflict, saying he is open to talks with the Taleban who ruled Kabul from 1996 to 2001. He finally emerged as president after signing a power-sharing deal with his poll rival Abdullah Abdullah.

The two men each claimed to have won fraud-tainted elections in a stand-off that caused political paralysis in Kabul and fanned worsening violence nationwide.

Ghani and Abdullah will fly to Brussels on Monday for NATO meetings, and on to London for a donor conference on Thursday designed to showcase the "national unity government" and demonstrate continuing international support for Afghanistan.

Afghan soldiers and police have suffered soaring casualties on the battlefield, with more than 4,600 killed this year as they take on the Taleban with less assistance from the US military.