Afghan president Ashraf Ghani called on the Taliban to "enter serious talks" with the government in Kabul Monday, following unprecedented marathon negotiations between the insurgents and the US in Qatar last week.

"I call on the Taliban to... show their Afghan will, and accept Afghans' demand for peace, and enter serious talks with the Afghan government," he said in a nationally televised address from the presidential palace in Kabul.

Afghan authorities have previously complained of being excluded from the discussions in Qatar, and warned that any deal between the US and the Taliban would require Kabul's endorsement.

However the Taliban have long refused to speak directly to Ghani's government, branding them "puppets".

Ghani spoke hours after his office released a statement saying that US special envoy Zalmay Khalilzad had assured them that the focus of the talks in Qatar remains finding a way to facilitate peace negotiations between the militants and Kabul.

Khalilzad arrived in Afghanistan late Sunday after six days of talks between Taliban representatives and US officials in Doha.

Both parties have cited "progress" as hopes rise that the unprecedented length of the negotiations could mean a deal paving the way for Afghan peace talks may be in sight, although sticking points remain.

"We want peace, we want it fast but we want it with a plan," Ghani continued Monday.

"We should not forget that the victims of this war are Afghans and the peace process should also be Afghan-led."