Afghan President Ashraf Ghani on Tuesday affirmed that Taliban will not be allowed to to derail the government in the country, besides extending last chance to come into national mainstream.
A massive truck bomb attack on Wednesday killed more than 80 people and wounded hundreds more, leading to violent protests over the lack of security.
According to Chief Executive of the Islamic Republic of Afghanistan, Abdullah Abdullah, who was among other government officials at the funeral at the time of the explosions, but was unharmed, the attack was a suicide bombing. The attack is the deadliest in Kabul since Taliban's ouster in 2001.
But the Afghanistan Cricket Board issued a strongly worded statement late on Wednesday, cancelling the matches in light of a truck bombing in the city's diplomatic quarter that killed at least 90 people.
A series of blasts in the country's capital last Saturday killed at least 19 people at a funeral for one of the victims of clashes between police and protesters a day before.
The Taliban has steadily expanded its reach since USA and North Atlantic Treaty Organisation forces formally concluded their combat mission at the end of 2014 and transitioned to a support and counterterrorism role.
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Officials see the Kabul Process as an attempt by the Afghan government to replace other processes on reconciliation like the Moscow meetings held since December 2016, and the American-backed Murree Process in Pakistan in 2015.
On Sunday, Adviser on Foreign Affairs Sartaj also said that the Afghan authorities should undertake a transparent investigation into the terror incident in order to make a determination about the perpetrators of the attacks based on concrete evidence.
However, he added that if the Taliban failed to take up the offer, Afghanistan would push for the United Nations to sanction the group as a "perpetrator and sponsor" of terror.
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The tense week of violence during the holy fasting month of Ramadan has left hospitals in Kabul overwhelmed, with many running beyond capacity to treat the injured.
He called for peace talks with the group.
"The Kabul administration wants peace talks only for the Taliban to surrender but this fake process will never succeed", said Zabihullah Mujahid in a statement sent to media, including VOA.