Over 22,000 Afghan families fled from their homes to escape fighting in the former Taliban bastion of Kandahar as authorities arrested four suspected insurgents over this week's rocket attack on Kabul, officials said on Sunday several foreign news agencies reported.

Since early May, violence has surged across several provinces including in Kandahar after the insurgents launched a sweeping offensive just days after the US-led foreign forces began their final withdrawal.

The Taliban's deadly assault has seen the insurgents capture scores of districts, border crossings and encircle several provincial capitals.

Dost Mohammad Daryab, head of the provincial refugee department said, "The fighting has displaced 22,000 families in the past one month in Kandahar. They have all moved from the volatile districts of the city to safer areas."

On Sunday, fighting continued on the outskirts of Kandahar city.

"The negligence of some security forces, especially the police, has made way for the Taliban to come that close. We are now trying to organise our security forces," said Lalai Dastageeri, deputy governor of Kandahar province.

Local authorities had set up four camps for the displaced people who are estimated to be about 154,000.

Kandahar resident Hafiz Mohammad Akbar said his house had been taken over by the Taliban after he fled. "They forced us to leave... I am now living with my 20-member family in a compound with no toilet," said Akbar.

Residents expressed concerns the fighting might increase in days ahead.

"If they really want to fight, they should go to a desert and fight, not destroy the city," said Khan Mohammad, who moved to a camp with his family.

Kandahar, with its 650,000 inhabitants, is the second-largest city in Afghanistan after Kabul.

Earlier this week, the chairman of the US joint chiefs of staff General Mark Milley said the Taliban appear to have "strategic momentum" on the battlefield.

But global rights group Human Rights Watch said there were reports the Taliban were committing atrocities against civilians in areas they had captured, including in the town of Spin Boldak near the border with Pakistan they captured earlier this month.

"Taliban leaders have denied responsibility for any abuses, but growing evidence of expulsions, arbitrary detentions, and killings in areas under their control are raising fears among the population," said Patricia Grossman, associate Asia director at HRW said in a statement.

The authorities meanwhile announced they had arrested four men they said belonged to the Taliban, accusing them of carrying out this week's rocket attack on Kabul.

"A Taliban commander, Momin, along with his three other men, have been arrested. They all belong to the Taliban group," ministry spokesman Mirwais Stanikzai told reporters in a video message.

At least three rockets landed near the palace on Tuesday as President Ashraf Ghani and his top officials performed outdoor prayers to mark the start of the Muslim holiday of Eid al-Adha.

The attack was however claimed by the jihadist Islamic State group.