A months-long diplomatic push by the United States to get the Taliban to talk to Kabul culminated in six days of meetings between the US and the militants in Doha, but the Taliban have long refused to negotiate with the Afghan government to end the 17-year conflict, AFP reported.
"I call on the Taliban to... show their Afghan will, and accept Afghans' demand for peace, and enter serious talks with the Afghan government," Ghani said in a nationally televised address from the presidential palace in Kabul.
Both the Taliban and the US cited progress over the weekend as hopes rise that the length of the negotiations could mean a deal may be in sight which paves the way for Afghan talks.
Sticking points remain, with topics including a cease-fire and a timetable for the withdrawal of foreign troops, as well as a prisoner exchange and a guarantee not to allow militant safe havens in Afghanistan believed to have been on the agenda.
US President Donald Trump's eagerness to withdraw troops from Afghanistan has also weighed heavy on the discussions.
But Afghan authorities have previously complained of being excluded from the talks in Qatar, and warned that any deal between the US and the Taliban would require Kabul's endorsement.
"We want peace, we want it fast but we want it with a plan," Ghani said in his address Monday.
"We should not forget that the victims of this war are Afghans and the peace process should also be Afghan-led... No Afghan wants foreign troops to remain in their country indefinitely. No Afghan wants to face suicide attacks in hospitals, schools, the mosques, and parks."
Ghani spoke hours after his office said it has been reassured by Washington that the talks in Qatar remain geared toward bringing the militants to the table with Kabul.
US Special Envoy Zalmay Khalilzad – who has been leading the negotiations – arrived in Afghanistan late Sunday to update officials including Ghani on the progress made.
"The US insisted in their talks with the Taliban that the only solution for lasting peace in Afghanistan is intra-Afghan talks," Khalilzad said, according to a statement released by Ghani's office.
"My role is to facilitate" such talks between the militants and Kabul, Khalilzad said according to Ghani, adding that the discussions are ongoing.
The palace said Khalilzad also confirmed that no agreement had been made on the withdrawal of foreign troops, adding that any such decision would be coordinated and discussed in detail with the Afghan government.
The Taliban have insisted foreign troops must pull out.
On Saturday Taliban spokesman Zabihullah Mujahid said that until a withdrawal timetable is decided progress on other issues is "impossible".
The palace's statement said Khalilzad denied reports that the issue of an interim government had been raised, saying that was "absolutely wrong" and there had been no discussions with the Taliban about any future government in Kabul.
He also confirmed there had been no progress on the issue of a cease-fire.