One policeman was also killed and two coalition soldiers were among some 16 people wounded, Zalmai Uriakhail, the police chief of Paktia province, told AFP, adding that the attack used an explosives-packed motorcycle.
The Nato-led International Security Assistance Force (Isaf) said it had no information on casualties but was looking into the incident.
Uriakhail said the attack occurred in a market in Chamkani district at about 11:00 am as pupils were leaving school after morning lessons.
"A suicide bomber on a motorbike detonated his explosives in a crowded area outside the school," he said. "The children had finished their studies and they were heading home."
The interior ministry confirmed the attack and said 10 children and a policeman were killed, with 15 children also injured.
The attack came hours after a roadside bomb killed seven members of a family in Laghman province, also in east Afghanistan.
Four women, two children and a man died when their car hit a Taliban-planted improvised explosive device (IED) near the town of Mehtarlam, Sarhadi Zwak, the provincial administration spokesman, said in a statement.
The Taliban, who ruled Afghanistan from 1996-2001, have repeatedly said they do not target civilians in their war against the US-backed government of President Hamid Karzai, but their attacks often kill non-combatants.
On Friday the insurgents issued a statement denying involvement in a suicide and gun attack on International Committee of the Red Cross (ICRC) offices in the eastern city of Jalalabad.
The statement repeated the declaration that the Taliban never target civilians.
Spokesmen for the insurgents were not immediately available to comment on Monday's attacks.
Eastern Afghanistan is a key battleground in the fight against the militants, many of whom use safe havens inside Pakistan to launch attacks against Afghan soldiers and the US-led military coalition.
For years, leaders in Kabul and Islamabad have traded accusations of blame over the extremists who pose a threat to security in both countries and cross the porous border with impunity.
There are presently around 100,000 international troops fighting the Taliban, with Afghan soldiers and police gradually taking over security responsibilities ahead of the withdrawal.
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The statement repeated the declaration that the Taliban never target civilians. , Cowardly liars.
The Taliban have always been a bunch of unscrupulous thugs drunk on the power of an imagined ideology of divine supremacy. These shining examples of ideal human conduct have done things like bombing the Bamiyan Buddhas, forcing minority community citizens to wear yellow patches (think Nazi Germany), providing refuge (and playing doting hosts) to Bin Laden, and committing numerous other random acts of wanton murder and terrorism. Then they went to open a franchise in neighboring Pakistan.And surprise surprise, the Pakistani version of the Talibs also has strikingly similar goals as their Afghan progenitors. Yet, you have people in Pakistan, political heavyweights, variously depicting the Taliban as being freedom fighters, rebels, Pashtun nationalists, etc. Yeah, peace talks will surely do the trick.
what a "Brave" act of Jehadis
PTI dharna in Kabul? Oh no, sorry, this wasn't a drone rather an act of a mujahid.