KABUL - The Kabul police chief resigned on Sunday after three Taliban attacks in 10 days on foreign guesthouses in the capital, while officials said Afghan forces had ousted insurgents who tried to seize former US and British base Camp Bastion in the south.

Taliban fighters breached the perimeter of Camp Bastion in the southern Afghan province of Helmand three days ago, just one month after the base was handed over to the Afghan army.

The attacks of recent days have renewed fears that Afghanistan's army and police are unable to secure the country.

The charity whose Kabul guesthouse was targeted in the latest such assault on Saturday, the US-based Partnership in Academics and Development (PAD, said on its website that three people were killed by insurgents who used guns and explosives.

They were identified as members of the same South African family - a father and his two teenage children - by a colleague of the mother, who survived the attack.

Kabul's police spokesman declined to comment on the reason for the chief's resignation. "We can only confirm... he will not continue his job as police chief anymore," Hashmat Stanekzai said.

Violence across Afghanistan has surged this year as the Taliban and their allies have stepped up their activities ahead of the scheduled withdrawal of most international troops by the end of next month.

Over the past 10 days, three compounds used by foreign organisations have been hit by armed attackers. In separate attacks in Kabul, two American soldiers, two British embassy workers and dozens of Afghan civilians have died.

The Taliban said on Saturday they had attacked the foreign guesthouse because they believed it to be a Christian centre. This was the second time this year the Taliban targeted a group that it said had links to Christianity.

PAD, which supports education in Afghanistan, could not be reached immediately for comment.

However, Partnership in Academics and Development (PAD), a small California-based education group, posted a message on its website saying three people had been killed in Saturday's attack on its compound.

"The attack... by multiple gunmen included one who detonated an explosive device killing three and injuring other staff members," the website said.

"In the midst of this unprovoked attack, Partnership in Academics and Development remains committed to providing educational resources for Afghan citizens."

The South African victims were members of a devout Christian family that had lived in Afghanistan for nearly 12 years, with the father running the charity and the mother working as a doctor, said a colleague at the Kabul clinic where the mother worked.

The 17-year-old son had been applying to universities in the United States. His sister was 14, said the colleague, who asked not to be identified for security reasons.

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

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

Meanwhile, Afghan soldiers finally ousted a group of Taliban from the former Camp Bastion. By Sunday, fighting at the base had ended and troops were clearing the area that had been seized by a few dozen insurgents, said Omar Zwak, a spokesman for the Helmand governor.

Further north in Helmand's Sangin district, a smaller army post was attacked and 12 soldiers killed in fighting on Friday and Saturday, Zwak said.

Camp Bastion was a key airfield for US-led NATO operations in the Taliban heartlands of the south.

President Ashraf 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 Taliban who ruled Kabul from 1996 to 2001.

Ghani finally emerged as president after signing a power-sharing deal with his poll rival Abdullah Abdullah.

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

Ghani was due to give a televised address on Sunday evening to announce that a deal had been reached over cabinet positions in the new government.

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

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

The US-led NATO combat mission in Afghanistan will end on December 31 and be replaced by a follow-on mission supporting the Afghan army and police, who have taken over responsibility for thwarting the Taliban.