A wave of attacks on Afghan police, army and NATO installations in Kabul killed at least 42 people and wounded hundreds, dashing hope that Taliban insurgents might be weakened by a leadership struggle after news of their longtime leader's death.

The attacks on Friday, which included a massive truck bomb in a heavily populated civilian area and a suicide attack on a police academy, were some of the most serious in months and the first in Kabul since the Taliban named a new leader last week.

They represent another blow to a tentative peace process that held its first meeting in July but was suspended last week.

Kabul has frequently been targeted by the Taliban and other insurgent groups seeking to destabilise the fragile government of President Ashraf Ghani although the scale of the latest attacks was unusually large.

Such a complex and coordinated set of attacks suggests a message from the Taliban at an especially delicate time following last week's revelation of Mullah Mohammad Omar's death and the subsequent leadership dispute.

"The question is, who is sending the message?" said Thomas Ruttig of the Afghanistan Analysts Network.

The Taliban are in the midst of a leadership dispute following last week's appointment of Mullah Akhtar Mansour as new leader. Mansour, who had previously been seen as open to peace talks, pledged to continue the insurgency that has killed and wounded thousands this year.

Ruttig said Mansour could be sending a message of resolve, with the latest Kabul attacks, to Taliban rank and file and to the Afghan government.

On the other hand, Taliban factions opposing Mansour's leadership could be seeking to kill any hope of future talks by launching their own wave of violence.

"The hope of some people was that the death of Mullah Omar would put the Taliban in disarray and possibly weaken them," Ruttig said. "I think that was a little over optimistic."

A Taliban spokesman claimed responsibility for the attack on the police academy in Kabul.

"The bomber was wearing a police uniform and detonated his explosives among students who had just returned from a break," a police official said.

At least 26 people were killed and 28 more wounded at the police academy, according to an Afghan police official who spoke on condition of anonymity.

A member of Afghanistan's residual NATO force was killed in an overnight battle at Camp Integrity, a base near Kabul's airport, said Colonel Brian Tribus, a spokesman for NATO's Resolute Support mission in Afghanistan.

The death marked the second international service member killed in Afghanistan this year after most foreign troops withdrew at the end of 2014, 13 years after the US-backed military intervention to topple the Taliban's Islamist regime.

The service member's nationality was not released.

The Afghan war between the Western-backed government and the Taliban has intensified since the NATO combat mission ended last year.