The death toll from multiple explosions outside a school in Afghanistan's capital Kabul has risen to 68, Afghan officials said on Sunday, with doctors struggling to provide medical care to 165 injured and officials trying to identify bodies.

Multiple blasts on Saturday evening — the deadliest in more than a year — shook the neighbourhood of Dasht-e-Barchi, home to a large community of Shi'ites from the Hazara ethnic minority — a regular target of militants.

At first, a car bomb was detonated in front of the Sayed Al-Shuhada school on Saturday, and when the students rushed out in panic, two more bombs exploded.

Officials said most of those killed were school girls. Some families were still searching hospitals for their missing children.

The blasts came as the United States military continues to pull out its last 2,500 troops from the violence-wracked country despite faltering peace efforts between the Taliban and Afghan government to end a decades-long war.

Describing Saturday's carnage, Interior Ministry spokesman Tareq Arian told reporters that a car bomb first detonated in front of the Sayed Al Shuhada School, and when the students rushed out in panic, two more devices exploded.

He said more than 100 people were wounded, adding that most of the victims were female students.

Residents were out shopping ahead of this week's Eidul Fitr, which marks the end of Ramazan, the Muslim holy month of fasting.

On Sunday relatives began burying the dead at a hilltop site known as “Martyrs Cemetery”.

No group has so far claimed the attack, but Afghan officials including President Ashraf Ghani blamed the Taliban.

“This savage group does not have the power to confront security forces on the battlefield, and instead targets with brutality and barbarism public facilities and the girls' school,” Ghani said in a statement after the blasts.

The insurgents have denied involvement and insist they have not carried out attacks in Kabul since February last year, when they signed a deal with the United States that paved the way for peace talks and withdrawal of the remaining US troops.

But the group has clashed in near-daily battles with Afghan forces in the rugged countryside even as the US military reduces its presence.

The United States was supposed to have pulled all forces out by May 1 under a deal struck with the Taliban last year, but Washington pushed back the date to September 11 — a move that angered the insurgents.

The top US diplomat in Kabul, Ross Wilson, called Saturday's blasts “abhorrent”.

“This unforgivable attack on children is an assault on Afghanistan's future, which cannot stand,” Wilson said on Twitter.

The Dasht-e-Barchi neighbourhood has been a regular target of attacks from Islamist militants.

In May last year, a group of gunmen attacked a hospital in the area in a brazen daylight raid that left 25 people dead, including 16 mothers of newborn babies.

On October 24, a suicide bomber blew himself up at a tuition centre in the same district, killing 18 people in an attack that also went unclaimed.