Afghan President Ashraf Ghani officially opened the Kabul Process meeting on Tuesday and said Afghanistan was on the frontline of terrorism in the world.
Ghani made the offer while addressing a peace conference he convened Tuesday in Kabul of regional and worldwide partners to discuss ways to end the deadly conflict in Afghanistan and boost cooperation to counter the Islamic State-led emerging regional threat of terrorism.
The violence comes as a regional summit is scheduled for Tuesday in Afghanistan to promote peace, security and reconciliation.
Rabbani survived an attack at the funeral of one of the protesters on Saturday, when a suicide bomb tore through a row of mourners and killed seven more people.
It is not clear who is behind the recent attacks.
It is probably time for the Afghans to decide themselves if they want to be ruled again by the Taliban, and, if they don't, or if they want some sort of coalition in Kabul that includes the Taliban, to take appropriate action themselves to bring the fighting and bombings to an end, without North Atlantic Treaty Organisation and the Americans.
Two days later, residents took to the streets to demand answers from the government, who they accused of security and intelligence failures.
"There is a big problem with the heads of the security institutions", said Salahuddin Rabbani, foreign minister and head of Jamiat-e Islami Afghanistan, the party behind Chief Executive Abdullah Abdullah. Ghani was referring to the bold step he had taken by visiting Pakistan amid tense ties when he took charge in September 2014.
On Friday, the district center again became a battlefield when hundreds of demonstrators incensed by the bombing clashed with police, prompting officials to beat them back with live rounds in the air, tear gas and water cannon.
Ghani also acknowledged that "Taliban-sponsored terrorism is creating a platform that is bringing terrorists to Afghanistan and Pakistan".
The real tragedy is that most distant states - but not the neighbours - are keen to wash their hands of Afghanistan.
"We are offering a chance for peace but this is not an open-ended offer".
As of late past year, the Taliban contested or controlled about 40 per cent of the country, according to US government estimates, leading some observers to doubt the group would be willing to negotiate any time soon.
A spokesman for the Taliban told Reuters news agency he had no comment to make on the conference.
Past attempts at peace talks have failed. But analysts say they want to regain momentum, against a back drop of separate peace talks engineered by Russian Federation.
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