By Khalid Abdelaziz

KHARTOUM (Reuters) - Sudanese rebels killed two children and wounded eight other civilians when they shelled the main town in Sudan's oil-producing South Kordofan state on Tuesday, the army said - the third bout of shelling in the past two weeks.

Sudan's army has been fighting SPLM-North rebels in the state, which borders South Sudan, since June last year, shortly before South Sudan seceded. But the South Kordofan capital Kadugli was until recently kept out of the fighting.

Army spokesman al-Sawarmi Khalid told Reuters the rebels had shelled an army garrison outside Kadugli but that some shells had landed inside the town.

He said the attack led to the killing of two children, while eight other civilians were wounded, adding that the army had launched an operation a few days ago to "cleanse" the area around Kadugli of rebels.

SPLM-North spokesman Arnu Lodi said the rebels had shelled army positions inside Kadugli after coming under government artillery fire.

"The government and our troops have been shelling each other since this morning," Lodi said. "They have been shelling our forces based outside Kadugli from inside the town and we are shooting back in self-defense."

A resident who declined to be named said several shells had landed in the center of the city. "People are frightened," he said.

Events in Sudan's border states are hard to verify as the government bans foreign media from travelling there.

The rebels first shelled Kadugli on October 8. At least one rocket hit a U.N. compound, prompting the United Nations to move its staff out of the town.

Khartoum accuses South Sudan of backing the rebels of the Sudan People's Liberation Movement-North, who fought as part of the southern rebel army during Sudan's civil war, which ended in 2005. South Sudan denies the accusation.

Fighting in South Kordofan and nearby Blue Nile state has displaced or severely affected 900,000 people, the United Nations said on Friday. Sudan agreed in August to let aid into rebel-held areas but the United Nations has been unable to win government approval to go ahead with distributing food.

Under international pressure, Sudan and South Sudan agreed last month to establish a buffer zone along their border after clashing along it several times in the past year. Indirect talks between Khartoum and the rebels, however, have made scant progress.

The SPLM-North last year formed an alliance with rebels in the western region of Darfur with the aim of toppling Sudan's veteran president, Omar Hassan al-Bashir, but it is unclear how closely the groups coordinate.

(This story is corrected with toll in paragraphs 1 and 4 to two children dead, eight people wounded)

(Additional reporting by Ulf Laessing; Editing by Kevin Liffey)