A blast hit a gathering of Taliban and Afghan security officials, meeting to celebrate the end of Ramadan fasting season, in the eastern city of Nangarhar on Saturday, officials said.
The Afghan government called for an extension to the ceasefire as it released Taliban prisoners on Saturday.
Afghans shared photos on social media purportedly showing Taliban fighters around the country gathering with security forces and locals for the holiday.
Taliban wearing traditional headgear entered Kabul through gates in the south and southeast. Traffic jams formed where people stopped to take pictures of the fighters with their flags.
Provincial police spokesman Shahpur Ahmadzai told The Associated Press that the Taliban were unarmed and no one was allowed into the city with weapons.
Atta-ul-Rahman Salim, deputy head of Afghanistan's High Peace Council, said Taliban fighters from across the country were entering government-controlled areas to visit their families "and they were being welcomed by government security forces".
Dozens of Taliban members on Saturday came to Kabul city from Maidan Wardak and Logar provinces.
Governors in Helmand, Kandahar and Zabul said both sides had adhered to the ceasefire and that there had been no reports of violence for 24 hours.
Earlier this week Taliban leader Akhundzada said he wanted direct talks with the United States before engaging in negotiations with the Afghan government.
The Taliban are fighting USA -led North Atlantic Treaty Organisation forces, combined under the Resolute Support mission, and the US -backed government to restore sharia, or Islamic law, after they were ousted by US -led forces in 2001. For many Afghans it has been first glimpse of peace in their lifetime.
It is for the first time the Taliban had agreed to a ceasefire for Eid, since the USA invasion in 2001. "It is hard to describe the joy", said Qais Liwal, a student in Zabul.
"Believe me I have never been so happy as I was about the ceasefire", Ahmad, a resident of Kabul said. "I can see Taliban walking around among ordinary people".
Photos on news websites showed armed police standing in line at the corner of the street hugging Taliban fighters one by one.
A video showed a huge crowd of people screaming and whistling as they welcomed the Taliban.
Since the beginning of the year, Taliban and Islamic State militants have staged 13 attacks in Kabul city, killing more than 300 people and wounding more than 500 others.
Insurgents were pictured playing alongside children and eating food together.
Two days after Ghani announced the ceasefire, Taliban, issued a statement and ordered its fighters not to clash with the Afghan security forces for the first three days of Eid.
The ceasefires, which follow months of deteriorating security, especially in the capital, Kabul, have coincided with the start of the soccer World Cup and the Afghan cricket team's test match debut against India.
The Taliban are fighting USA -led North Atlantic Treaty Organisation forces, combined under the Resolute Support mission, and the US -backed government to restore sharia, or Islamic law, after their ouster by US -led forces in 2001.
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