The new audio message was distributed to media by the Taliban group spokesman Zabiullah Mujahid.
Sirajuddin Haqqani who is the also the deputy supreme leader of the Taliban group, rejects that the network was involved in the recent deadly attacks.
He claims that the attack close to Zanbaq square near the embassy of Germany was not plotted and carried out by the Haqqani network of the Taliban group.
Haqqani also claims that the network and the Taliban insurgents never carry out attacks in public areas.
He also vowed that the Taliban insurgents will continue to their fight until all foreign forces fully withdrawn from the country.
The first incident in the city took place on 31st of May, after a vehicle packed with explosives was detonated leaving more than 150 people dead and over 400 others wounded.
A coordinated suicide attack also rocked Kabul city two days after the incident as scores of people had gathered in the funeral ceremony of Salim Izadyar, the son of the deputy house speaker of the Afghan Senate House, who was killed during the rallies organized to protest against the attacks and failure of the government and security institutions to ensure security for the people.
The Afghan intelligence said the directorate has credible information suggesting that the attacks were plotted and carried out by the Haqqani network based in Pakistan.