At least four Afghans have been killed as police fired live rounds to disperse protesters seeking to march on the presidential palace and demand the government’s resignation after a devastating truck bombing.

Hundreds of demonstrators calling for the president, Ashraf Ghani, to step down and chanting “death to the Taliban” clashed with police near the site of the explosion on Wednesday in Kabul’s diplomatic quarter, which killed at least 90 people and injured more than 460.

Security officials responded with live rounds, teargas and water cannon as the protesters tried to overrun a security cordon on Friday in the Afghan capital.

Kabul has been on edge since the bombing, which showed militants could strike the highly secure diplomatic district, home to the presidential palace and foreign embassies surrounded by concrete blast walls.

With anger mounting, Afghans are demanding answers from the government over perceived intelligence failures leading to the bombing, which underlines growing insecurity in Afghanistan.

Rahila Jafari, a civil society activist, said: “Our brothers and sisters were martyred in the bloody attack and our leaders are doing nothing to stop this carnage. We want justice, we want the perpetrators of the attack to be hanged to death.”

Demonstrators throw stones at security forces days after 90 people were killed in a truck bombing in Kabul. Photograph: Massoud Hossaini/AP

Another protester said the demonstrations would continue until Ghani and the Afghan 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.

Ghani is expected to approve the execution of 11 Taliban and Haqqani prisoners, a government source said, apparently in retaliation.

The Taliban, who are conducting their annual spring offensive, have denied involvement.

The Haqqani network, which is long thought to have ties to Pakistan’s military establishment, is led by the Taliban deputy leader, Sirajuddin Haqqani.

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