The Taliban already roam huge swaths of the country and, with foreign troop levels of about 15,600, down from 140,000 in 2014, there appears little hope of outright government victory.
The Afghan Taliban had announced that its three-day ceasefire will indeed end at midnight local time Sunday, dispelling reports that it might be extended.
No group has claimed responsibility for the blast, which happened outside the governor's office in the eastern Afghan province of Nangarhar, wounding at least 30 others, a security official said.
In the contested district of Bati Kot in Nangarhar, Taliban fighters carrying assault weapons and rocket-propelled grenade launchers traveled by auto and motorbike, waving Afghan and Taliban flags.
The Taliban had agreed to a truce but only for the first three days of Eid, which started Friday, promising not to attack Afghan soldiers or police. Daesh was not included in the government´s ceasefire.
President Ashraf Ghani said he would extend a government ceasefire on Saturday and urged the Taliban to do the same, winning praise at home and global backing, but critics said his overtures had allowed the Taliban to pour into cities unchecked.
It was not clear if Ghani knew about the bomb in the east when he made his address.
The Taliban are fighting US -led North Atlantic Treaty Organisation forces, combined under the Resolute Support mission, and Ghani's USA -backed government to restore sharia, or Islamic law, after their ouster by US -led forces in 2001.
Mr Pompeo added: "The United States is prepared to support, facilitate, and participate in these discussions".
The Taliban announced the three-day halt to hostilities earlier this month, days after a unilateral ceasefire lasting until Wednesday was ordered by the government. Laskargah, where the Taliban have delivered a series of blows to government forces this year.
The Afghan government declared the ceasefire in honor of Eid al-Fitr, which marks the end of Ramadan.
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. The Taliban urged people to come forward and pose for the camera.
"The incident has nothing to do with the Taliban", spokesman Zabihullah Mujahid told Reuters. They were unarmed and were met with greetings and hugs by civilians and soldiers as the war-torn county is seeing an unprecedented ceasefire for the Eid holiday.
Afghan media outlets such as television stations ToloNews and Ariana News showed Interior Minister Wais Ahmad Barmak allegedly meeting Taliban militants in the eastern Kabul neighbourhood of Company.
Ghani also said 46 Taliban prisoners had been released, a trend that "is going to continue".
"There are some people in government or among the Taliban that will not see the benefit of the ceasefire and will create some problems", Khpalwak said, adding that "we thank the government, Taliban and people for the ceasefire and all the credit of this ceasefire goes to the people of the country".
"Good steps for peace have been taken, but more steps have to be taken", said council chairman Karim Khalili.
It was the first formal nationwide ceasefire since the 2001 U.S. invasion and the display of jubilation and unity has fuelled hopes among war-weary Afghans that peace is possible. "It is hard to describe the joy".
The UN secretary general's special representative for Afghanistan, Tadamichi Yamamoto, wrote in the Washington Post: "I truly believe the outlines for a peace deal are now discernible through the haze and dust of war". "I saw Taliban and police standing side by side and taking selfies".
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