"The Shegeg Karo school was hit and one classroom was destroyed. It was in session. The youngest child to die was five-year-old Yusuf Adam Hamid," said the statement.
The aid organisations said that two other children were seriously wounded and another 30 lightly injured.
Ahmed Hussein Adam, the London-based spokesman for the rebel group Justice and Equality movement (JEM), said: "There has been continuous bombardment by Antonov aircraft for three days.
"On Sunday morning, they bombarded a village in the area of Al-Ain and killed three children of the local leader Sheikh Mahmud Bakr and injured another one," Adam said.
He claimed government had also destroyed wells and other water resources in the aerial bombardment.
According to the JEM, Sudanese forces also bombed a busy market area.
"Yesterday afternoon they killed 11 civilians and injured three women and two children when they bombed the market in Shugag Karo, near Deir Maza," Adam said.
"It was market day and there were a lot of people concentrated in one place."
Adam said the attacks deliberately targeted civilians as "there was not a single armed element from the rebel movements in the area".
"It is very clear that the government of Sudan does not want to go for any political solution, they just want to impose a military solution," Adam said.
The Sudanese army has not confirmed the bombardment.
The Sudanese army has always denied bombing in the area, which would have been a violation of a UN Security Council resolution.
However, only last week, a joint UN-African Union peacekeeping mission confirmed earlier rebel reports of bombing in North Darfur, in spite of government denials.
Meanwhile, the transitional regional authority for Darfur, led by Mini Minawi, a former rebel leader who signed a peace deal with the government two years and became a senior presidential assistant, said it would suspend its participation in the national unity government for a day.
The decision was in protest over what the authority says is the slow pace in implementing the peace deal.
Minawi listed a number of obstacles that had delayed the implementation of the agreement.
The list included the failure to disarm the Janjawid, ongoing arrests, and the absence of development projects in Darfur and other regions.