Afghan President Ashraf Ghani has accused Pakistan of sending "messages of war" and harbouring bomb-making camps, after a wave of devastating blasts in Kabul killed at least 56 people.

Ghani said on Monday that Pakistan has failed to rein in the Taliban, as peace talks falter and armed groups step up attacks that are testing beleaguered Afghan security forces.

"Pakistan still remains a venue and ground for gatherings from which mercenaries send us messages of war," Ghani said.

"The last few days have shown that suicide bomber training camps and bomb-producing factories which are killing our people are as active as before in Pakistan. We can no longer see our people bleeding in a war that is exported from outside."

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The Afghan leader made the call as another car bomb exploded on Monday outside the airport in Kabul, killing five people and injuring another 20, including women and children.

The Taliban claimed responsibility for the attack in a message to Al Jazeera.

Taliban fighters are stepping up their summer offensive amid a bitter leadership dispute following the announcement of the death of longtime leader Mullah Omar.

Since coming to power last year Ghani has actively courted Pakistan, which has historically backed the Taliban, in what experts call a calculated gambit to pressure the armed group to the negotiating table.

Ghani's sharp rebuke of Afghanistan on Monday indicates a change in tactic in dealing with Pakistan.

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In Monday's attack a suicide car bomber tore through a crowd during the lunchtime rush at a checkpoint where passengers usually undergo the first round of body checks before entering the airport.

The Taliban said two vehicles belonging to foreign coalition forces were the target.

Al Jazeera's Jennifer Glasse, reporting from Kabul, said that with the latest attack, the Taliban was trying to prove that it had a presence in the capital.

Monday's was the latest in a series of bombings in the city which began on Friday with three blasts - one close to an army complex, another at a police academy and one at a US special forces base - killing a total of 51 people.

Pakistan has historically supported the Taliban, and many Afghans accuse it of continuing to nurture sanctuaries on its soil in the hope of maintaining influence in Afghanistan.

"In my telephone call with [Prime Minister Nawaz Sharif on Sunday], I told Pakistan to see terrorism in Afghanistan the same way it sees terrorism in Pakistan," Ghani said.

"I ask the Pakistani government if the mass killings of Shah Shaheed had happened in Islamabad and the perpetrators were in Afghanistan, what would you do?" he said, referring to a Kabul neighbourhood that suffered a fatal truck bombing on Friday.