The Taliban on Wednesday claimed responsibility for a huge bomb attack in Kabul targeting the defence minister as the insurgents fought for control of a string of besieged cities.

The bomb-and-gun attack on Defence Minister Bismillah Mohammadi Tuesday was one of the biggest in Kabul for months, bringing violence to the capital after intense fighting in the south and west of the country.

The Afghan and US militaries have carried out airstrikes against the insurgents to push them back, and the Taliban said the Kabul attack was a response to that.

"The attack is the beginning of the retaliatory operations against the circles and leaders of the Kabul administration who are ordering attacks and the bombing of different parts of the country," Taliban spokesman Zabihullah Mujahid said in a statement on social media.

It represents a major escalation by the Taliban, who have largely refrained from large-scale attacks in the capital in recent years after starting talks with the United States on troop withdrawal.

The Tuesday attack targeted Mohammadi as well as some lawmakers.

The first bomb exploded in the centre of Kabul, sending a thick plume of smoke into the sky, AFP correspondents reported.

Less than two hours later, there was another loud blast followed by smaller explosions and rapid gunfire, also near the high-security Green Zone that houses several embassies, including the US mission.

The minister was safe and Afghan forces repelled the attackers, but at least eight people were killed, according to interior ministry spokesman Mirwais Stanikzai.

Mohammadi later said it was a suicide car bomb attack targeting his house.

A security source said several attackers stormed a lawmaker's house after setting off the car bomb and shot at the residence of the defence minister from there.

Security forces had cordoned off the scene of the attack on Wednesday as troops inspected the buildings and cars damaged by the blasts.

Rubble covered the area while there were bloodstains on some of the floors.

There was little respite in Kabul early Wednesday after a blast injured three people, according to police.

- 'No way to escape' -
The Taliban threat came after the Afghan military launched a counterattack against the insurgents in the southern city of Lashkar Gah.

The military had asked people to leave the city on Tuesday as they prepared for their offensive.

Resident Saleh Mohammad said hundreds of families had fled as fighting erupted between the two sides, trapping many in the crossfire. 

"There is no way to escape from the area because the fighting is ongoing. There is no guarantee that we will not be killed on the way," Mohammad said.

"The government and the Taliban are destroying us."

The insurgents have taken control of vast swathes of the countryside and key border towns, taking advantage of the security vacuum left by the withdrawal of US forces.

The Taliban are now targeting cities, with fierce fighting for a week around Herat near the western border with Iran, as well as Lashkar Gah and Kandahar in the south.

The Afghan military counterattack came after another night of heavy clashes with the Taliban.

"Those families which had financial support or a car have left their homes. The families who can not afford to are obliged to stay in their own homes as we are," resident Halim Karimi told AFP.

"We don't know where to go or how to leave. We are born to die."

The loss of Lashkar Gah, the capital of southern Helmand province, would be a massive strategic and psychological blow for the government.

The United Nations reported Tuesday that at least 40 civilians had been killed in Lashkar Gah in the previous 24 hours.

- 'War crimes' -
Meanwhile, Human Rights Watch accused that the Taliban of "summarily" executing detained soldiers, police and civilians with alleged ties to the Afghan government in areas they had recently seized.

The rights group said it had also obtained a list of 44 people who were killed by the Taliban in the town of Spin Boldak, which the insurgents captured last month along the border with Pakistan.

"Taliban commanders with oversight over such atrocities are also responsible for war crimes," Patricia Gossman, associate Asia director at HRW said in a statement.

Washington and London have also accused the insurgents of committing atrocities that may amount to "war crimes" in Spin Boldak.

 Turkey reacts to US plan
Ankara has criticised a US plan to use third countries such as Turkey to resettle thousands of Afghans who risk being targeted by Taliban insurgents over their US links.

Less than a month before the United States is set to end its longest-ever war, the State Department on Monday announced a new refugee admissions programme for Afghan nationals.

The programme covers interpreters and translators who worked with US forces, Afghans involved with US-funded projects and those employed by US-based NGOs or media organisations. 

It involves resettling the Afghans in third countries in the region for around a year while their paperwork is processed.

But Turkey, which is already home to more than four million migrants -- most from war-torn Syria -- said it was never consulted.

"It's unacceptable to seek a solution to the problem in our country without our country's consent," the foreign ministry said in a statement issued late Tuesday.

The State Department referred to Turkey as one possible relocation point, also mentioning Pakistan.

But the Turkish ministry said the US plan would lead to a "big migration crisis in our region", adding it lacked the capacity to deal with "a new migration crisis on behalf of a third country".

With the ongoing withdrawal of US and NATO forces from Afghanistan, Turkey fears a new influx of refugees. 

President Recep Tayyip Erdogan has said Turkish officials were holding high-level talks over the issue with Afghan counterparts. 

The issue is also likely to feature in talks between Ankara and Brussels about updating a 2016 deal under which Turkey received aid for hosting migrants seeking refuge in the Europe Union.

Asked about the number of Afghan arrivals in Turkey, a senior State Department official said on Monday: "I don't have numbers on Turkey.

"I would say we haven't seen major large outflows of people yet, but we have seen some numbers of people crossing, but not large numbers yet."

The Turkish foreign ministry said if the US wanted to take in the Afghans, it could do so through "direct flights".