The incident happened near Cham Chaka village southeast of Abu Kershola, said Nuba Reports, a website of “citizen reporters” in South Kordofan’s Nuba Mountains battleground.
It said the explosion happened when a group of youngsters found an unexploded rocket-propelled grenade.
“The children picked up the round and it exploded, killing nine of the children and wounding five,” Nuba Reports said.
The incident happened in a remote area on July 24 and was posted on the website late Sunday.
On Monday night the website’s founder, Ryan Boyette, gave AFP names of the victims, who he said were between three and 14 years old.
The Sudan Revolutionary Front rebel alliance seized Abu Kershola in April during coordinated strikes in the area, which analysts said humiliated the authorities.
The military took one month to retake Abu Kershola.
Ethnic rebels of the Sudan People’s Liberation Army-North (SPLA-N) have been fighting for two years in South Kordofan, and are part of the alliance seeking to topple the Khartoum government.
Sudan severely restricts access by journalists and other foreigners to South Kordofan and Blue Nile state, where SPLA-N is also fighting.
There are no reliable figures for how many people have died in the war but the UN has said more than 200 000 have fled the area as refugees.