Hawzah News Agency (Kabul - Afghanistan), President Ashraf Ghani appealed to the militants to follow the government's lead and enter peace talks, reported BBC.
In extraordinary scenes, militants have been embracing security force members and taking selfies with citizens.
However, 25 people died on Saturday in a suicide attack on one gathering of Taliban and government officials in Nangarhar.
Taliban members and local residents were among the victims of the attack, province spokesman Attaullah Khogyani told BBC, adding that 54 people were wounded.
Daesh (ISIS) terrorist group, which is active in the area, said it carried out the attack.
In a TV address, Ghani said the government was ready for 'comprehensive negotiations' with the Taliban.
'All those issues and demands that have been put forth we are ready to discuss at the peace talks,' he said.
The past day, where Taliban and government forces and officials mingled during Eid al-Fitr, the end of the holy fasting month of Ramadan, 'proved that we are all for peace', Ghani said.
During the ceasefire, Taliban militants could receive medical and humanitarian assistance and Taliban prisoners could see their families, he added.
The government has also released some Taliban prisoners, Ghani said.