The victims were caught in the blast as they traveled in a car on a shopping trip ahead of the Muslim holiday of Eid this weekend, a relative, Qimat Khan, told Associated Press Television at the scene of the bombing in the eastern province of Khost.
Initial reports indicated the bomb had been beneath a water truck, but officials later clarified it was planted beneath a water tank in the Matun area of Khost city.
Taher Khan Sabari, deputy governor of Khost, said the dead children included a boy aged about 1 year, and a girl of about 3 years old. The other children were older, he said.
The Interior Ministry initially said two children and a man had been killed and another three people, including two children, had been wounded in the Tuesday morning attack.
Khan, the relative, said the wounded later died of their injuries.
Wazir Pacha, a spokesman for the provincial police chief of Khost, said authorities were investigating what the target might have been.
Taliban violence against U.S. and NATO soldiers and Afghan civilians continues to rise.
A U.S. service member was killed on Monday in an insurgent attack in the south of the country, NATO said Tuesday. It did not give any further details of the attack or where it occurred. The death comes a day after NATO announced four U.S. service members were killed in separate attacks - three Sunday and one Monday.
The latest death brings to 16 the number of U.S. troops killed in Afghanistan this month. October was the deadliest month for the U.S. military in the eight-year war with 58 service members killed.
Military officials and others expect President Barack Obama to make a decision soon to deploy 32,000 to 35,000 more U.S. forces. The top U.S. commander in Afghanistan, Gen. Stanley McChrystal, has asked for about 40,000 extra U.S. troops to be sent to Afghanistan, in addition to the 68,000 already in the country.
Separately, the Interior Ministry said police seized a weapons cache with 174 mortar rounds in the far northeastern province of Badakshan.
The Defense Ministry said 21 suspected insurgents were arrested by the Afghan army and international forces in separate operations in Khost and the southern province of Kandahar in the past 24 hours.