Kabul - The head of the Taliban-allied Haqqani network has ruled out any involvement in a wave of deadly bombings in Kabul, reiterating the group's denial as it faces widespread condemnation.

The Afghan government has blamed the Haqqani network for a catastrophic truck bombing in Kabul's diplomatic quarter on May 31, the deadliest in the Afghan capital since 2001 which killed more than 150 people.

The Taliban disavowed any responsibility soon after the explosion, with Taliban deputy leader Sirajuddin Haqqani repeating the denial in an audio message posted on the group's website on Sunday.

"We have already condemned the (attacks). The Islamic Emirate (Taliban) is not behind them," he said. "The enemy wants to defame Mujahideen and create a distance between the nation and Mujahideen."

The bombing triggered angry protests and street clashes in Kabul on June 2, prompting police to respond with live rounds that left at least four people dead.

A day later, at least seven people were killed when suicide bombers tore through a row of mourners who were attending the funeral of one of the protesters. The statements ruling out any Taliban hand in the bombings have fallen on sceptical ears in Kabul.

"Despite the Taliban's categorical denial, the attack bears all the hallmarks of the movement," Borhan Osman of the Afghanistan Analysts Network wrote in a recent assessment of the May 31 bombing. "The movement's operational capacity and logistical access to plan and execute such a bombing is beyond question."

Haqqani also rejected it was behind a bombing near the Grand Mosque in western Herat city on June 3, which left seven people dead and 16 others wounded. "Even if such incidents... have happened in the past, we have apologised and asked people for forgiveness," Haqqani said.

Since the Kabul truck bombing, protesters have set up sit-in camps in at least six locations around the capital, including one near the bombing site, demanding the resignation of President Ashraf Ghani's government. In an apparent effort to appease the protesters, the Afghan government on Sunday sacked two top security officials including Kabul police chief over the killing of demonstrators on June 2.

Afghan civilians killed as US troops open fire after bomb attack

As many as three Afghan civilians were killed on Monday when American troops opened fire after their vehicle struck a roadside bomb, an official in Nangarhar province said.

A man and his two sons were killed at their home in Ghani Khel, a district in the south of Nangarhar, on the border with Pakistan, said Attaullah Khogyani, a spokesman for the provincial governor.

"After the bomb blast hit them, the American forces then started shooting and killed one man and two children nearby," he said. The US military command in Kabul said a convoy of American and Afghan troops was struck by a roadside bomb and attacked by gunmen. "The convoy returned fire in self-defence and there were no US casualties," the command said in a statement.

There had been no official report of civilian casualties filed, but the military was investigating the incident, the US military said in a statement. "We take civilian casualties very seriously and all allegations are thoroughly investigated," it said.

Civilian casualties have run at near record highs as fighting spreads to more areas of Afghanistan, according to the United Nations.

Afghan President Ashraf Ghani generally has been less vocal than his predecessor, Hamid Karzai, in publicly criticising the US military when troops are involved in incidents where civilians are killed. On Saturday, three American soldiers were killed and one wounded when an Afghan soldier opened fire on them in Nangarhar, where elite US troops have been helping Afghan forces battle Islamic State militants. Also over the weekend, an American air strike in southern Afghanistan killed at least three Afghan policemen and wounded several during a joint operation by Afghan and US special forces.

US and Afghan troops have been battling militants in Nangarhar province for months. Islamic State, or Daesh as it is known in Afghanistan, has established a stronghold in the region, which borders Pakistan. US military officials estimate there are about 600 to 800 Islamic State fighters in Afghanistan, mostly in Nangarhar, but also in the neighboring province of Kunar.

The increase in involvement by U.S troops and warplanes comes as US President Donald Trump's administration weighs whether to deploy more troops in the war-torn country. Reuters reported in late April that the US administration was carrying out a review of Afghanistan and there were conversations over whether to send between 3,000 and 5,000 US and coalition troops to Afghanistan.

Deliberations include giving more authority to forces on the ground and taking more aggressive action against Taliban fighters. This could allow US advisers to work with Afghan troops below the corps level, potentially putting them closer to fighting, a US official said.