The pause in fighting, only the second of its kind in Afghanistan's nearly 19-year-old war, appeared to be holding on day two after the government welcomed the truce by announcing plans to release up to 2,000 Taliban inmates.
President Ashraf Ghani said his administration was also ready to hold peace talks with the Taliban, seen as key to ending the war in the impoverished country.
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"The government of Afghanistan has today released 100 Taliban prisoners from Bagram prison," National Security Council spokesman Javid Faisal told AFP.
He said the prisoner release was to "help the peace process" and will continue until 2,000 prisoners are freed.
Faisal said there had been no reports of any ceasefire violations so far, adding that authorities plan to release insurgent prisoners in batches of 100 daily.
"We hope this will eventually lead to a lasting peace that the people of Afghanistan so much desire and deserve," he said.
In the northern city of Kunduz, which the Taliban attacked just days ago, calm prevailed as residents celebrated Eid at the end of the holy month of Ramadan.
"Just two days ago panic had set in the city," said Atiqullah, a shopkeeper from Kunduz.
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"Today, you go out and feel as if there is no more fighting. People are actually celebrating Eid."
The current ceasefire is the first initiated by the Taliban. The only other comparable pause came over Eid in 2018, and was first offered by Ghani.
'Goodwill gesture'
The normally restive southern province of Uruzgan was also calm, police said.
"There was non-stop fighting every single day, but since the ceasefire was announced not a single shot has been fired," said Haji Lal Agha, the provincial police chief.
"It is especially good for the residents of Trinkot who would hear the sound of gunfire every day," he added, referring to the provincial capital.
There were no reports of fighting from Kandahar, once a bastion for the Taliban, and the southeast province of Khost was also peaceful, police said.
"We are carefully monitoring the ceasefire and the situation, and there has not been any major activity by the enemy since the ceasefire was announced," interior ministry spokesman Tareq Arian said.
He said they were, however, investigating a mortar attack on Sunday in Laghman province that killed five civilians.
Violence had escalated since the Taliban signed a deal with Washington in February to withdraw all US forces from the country by next year.
The agreement also set the stage for intra-Afghan peace talks and stipulated that the government would first release up to 5,000 Taliban prisoners, while the militants would free about 1,000 national security personnel.
Before Sunday's announcement to free up to 2,000 Taliban prisoners as a "goodwill gesture", Kabul had already released about 1,000 Taliban inmates while the insurgents had freed about 300 Afghan security force captives.
The Taliban insist Kabul must release all 5,000 members as agreed in the deal with the US.
"This process should be completed in order to remove hurdles in the way of commencement of intra-Afghan negotiations," Taliban spokesman Suhail Shaheen said on Twitter.
US Secretary of State Mike Pompeo has welcomed the ceasefire, but insists the freed Taliban prisoners should not return to the battlefield.
A motorist is checked by security at a checkpoint in the Afghan capital at the start of the Eid al-Fitr holiday
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