Saturday's attack, which also took place in Jalalabad, killed at least 36 people and wounded 65, according to Kamawal, director of the provincial health department.
Some have criticized his move, which allowed the Taliban to flow into cities across the country, though the militants said they would withdraw by sunset on Sunday.
In a statement Saturday, U.S. Secretary of State Mike Pompeo welcomed Ghani's offer of an extension to the cease-fire, adding that the U.S. "stands ready to work with the Afghan government, the Taliban, and all the people of Afghanistan to reach a peace agreement and political settlement that brings a permanent end to this war".
"They are unarmed, as they handed over their weapons at the entrances", Kabul police spokesperson Hashmat Stanekzai told Reuters.
The Taliban announced a ceasefire for the first three days of Eid, which started Friday, promising not to attack Afghan security forces for the first time since the 2001 USA invasion.
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The militants even met Afghan Interior Minister Wais Ahmad Barmak in the capital, TOLO news reported.
As news of the attack spread, Afghan President Ashraf Ghani announced he would extend the cease-fire with the Taliban, but did not give a time frame for the extension. "Everyone is exhausted of war and if our leaders order us to continue the ceasefire, we will hold it forever".
Speaking from his palace in a solemn and serene tone, Ghani said his government was ready for "any kind of peace and any kind of talks", and that he would be willing to discuss all Taliban concerns, including "the future role of global troops" in the country.
Khogyani said a suicide bomber on foot had targeted Taliban, local elders and civilians as they left the governor's compound where they had attended a special event for the Eid holiday.
Ghani said the current ceasefire will be extended from the fourth day of Eid.
Ghani also repeated his promise that everything could be on the negotiation table, including the presence of foreign forces.
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That came after Ghani announced that police and troops would cease operations against the Taliban for eight days, starting last Tuesday - though he warned that operations against other militants, including Daesh, would continue.
"We are calling on the Taliban, they saw in the media that in villages and districts and all parts of the country people called for the ceasefire to be extended extending and for directs talks".
Ghani also urged the Taliban to extend its three-day cease-fire, which was set to end on June 17.
"I'm 40 years old and this is the best Eid I've had in my entire life", one Kandahar resident said on a BBC radio phone-in. Most of the dead and wounded were believed to be Taliban, he said. But they have refused to meet with the US -backed government, saying they will only negotiate with the United States directly.
"We have no intention to extend the ceasefire".
Government officials urged the militants not to return to fighting, as dozens of unarmed Taliban exchanged Eid greetings with soldiers and civilians.
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