Afghanistan police on Friday fired live rounds to disperse hundreds of stone-throwing protesters seeking to march on the presidential palace to demand government's resignation following a catastrophic truck bombing that killed 90 people and wounded hundreds.

Public anger has mounted after the brazen attack, the deadliest in the city since 2001, which was launched from an explosives-laden sewage tanker that tore a massive crater in the ground.

Demonstrators calling for President Ashraf Ghani to step down and chanting "Death to the Taliban" clashed with police near the bombing site, prompting officials to respond with live rounds, tear gas and water cannon as some protesters tried to overrun a security cordon.

At least three protesters were wounded, some of them critically, and were rushed to Kabul's Emergency Hospital, witnesses said.

The bombing during the holy month of Ramadan highlighted the ability of militants to strike even in the capital's most secure district, home to the presidential palace and foreign embassies that are enveloped in a maze of concrete blast walls.

Angry citizens have demanded answers from the government over the perceived intelligence failure leading to the assault, which underscores spiralling insecurity in Afghanistan.

"Our brothers and sisters were martyred in the bloody attack on Wednesday, and our leaders are doing nothing to stop this carnage," Rahila Jafari, a civil society activist, said during the protest.

"We want justice, we want the perpetrators of the attack to be hanged to death." 

Another enraged Afghan said the protests would continue until Ghani and Chief Executive Abdullah Abdullah resign. "Day after day, innocent civilians are being killed by terrorists.

If our leaders cannot restore security they should step down," he said.

Afghanistan's intelligence agency has blamed the Taliban-allied Haqqani Network for the attack.

Afghan President Ashraf Ghani is expected to approve the execution of 11 Taliban and Haqqani prisoners, a government source told AFP, in apparent retaliation to the assault.

The Taliban — currently in the midst of their annual "spring offensive" — denied they were involved.

The Haqqani Network, long thought to have ties to neighbouring Pakistan's shadowy military establishment, is led by Sirajuddin Haqqani — who is also the Taliban's deputy leader.

It has carried out numerous attacks in Kabul, including the 2008 Indian embassy bombing that killed almost 60 people.