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The explosion rocked the west Kabul district of Dasht-e-Barchi - a regular target of Sunni Islamist militants - as residents were out shopping ahead of Eid-al-Fitr next week that marks the end of Ramadan, the Muslim holy month of fasting.

It comes as the United States military continues to pull out its last from violence-wracked Afghanistan, despite faltering peace efforts between the Taliban and Afghan government to end a decades-long war.

"More than 30 students and other countrymen have been killed, and over 50 more were wounded. The toll is rising." interior ministry spokesman Tareq Arian told reporters.

Arian's deputy Hamid Roshan told AFP that an investigation had begun into the explosion.

"I saw many bloodied bodies in dust and smoke, while some of the wounded were screaming in pain," Reza, who escaped the blast, told AFP, adding that most of the victims were teenaged female students who had just left the school.

"I saw a woman checking the bodies and calling for her daughter. She then found her daughter's blood stained purse after which she fainted and fell to the ground."

Health ministry spokesman Dastagir Nazari said several ambulances had been rushed to the site and were evacuating the wounded.

He said an angry crowd had beaten the ambulance workers at the site.

No organisation took responsibility for the attack and the Taliban denied involvement.

But President Ashraf Ghani blamed the group for the blast, which took place near the entry gate of Sayed Al-Shuhada girls' school.

"This savage group (Taliban) 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," he said in a statement.

'Despicable act of terrorism'

The Taliban has denied carrying 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 in the rugged countryside with Afghan forces 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 the blast "abhorrent", tweeting: "With scores murdered, this unforgivable attack on children is an assault on Afghanistan’s future, which cannot stand."

The European Union delegation in Afghanistan condemned what it said was a "despicable act of terrorism".

"Targeting primarily students in a girls' school, makes this an attack on the future of Afghanistan. On young people determined to improve their country," it said on Twitter.

The United Nations Assistance Mission in Afghanistan (UNAMA) expressed its "deep revulsion" at the blast.

And Pakistan's foreign ministry called the attack "reprehensible" and vowed to support Afghanistan in its peace efforts.

The Dasht-e-Barchi neighbourhood has been a regular target of attacks from Sunni 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 killed, including 16 mothers of newborn babies.

The hospital was supported by the international medical charity Doctors Without Borders, which later pulled out of the project.

No group claimed that attack, but Ghani blamed the Taliban and the jihadist Islamic State group.

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

Agencies contributed to this report.

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