JUBA (Reuters) - South Sudan's army launched a military offensive against insurgents loyal to rebel leader David Yau Yau in the eastern Jonglei state, killing 28 militants, authorities said on Tuesday.

Yau Yau raised a rebellion last year, with support from his Murle ethnic group, after losing local elections in 2010.

Revenge killings between Murle and Lou Nuer tribesmen and a heavy-handed government disarmament campaign meant that peace talks between Juba's government and Yau Yau never got off the ground.

"The operation has started," army spokesman Philip Aguer told Reuters. "The community leaders had been given time to make an agreement to get Yau Yau to return but those attempts have failed."

Since winning independence from Sudan in July 2011, South Sudan has been struggling to assert law and order across vast swathes of territory bristling with weapons after the 1983-2005 civil war with Khartoum.

South Sudan's army has clashed repeatedly with rebels in Jonglei, where Total holds a vast oil concession.

Aguer said 28 rebels were killed on Monday in clashes around Kongkong, several kilometers (miles) east of the town of Pibor.

Pibor district commissioner Joshua Konyi said civilians have been advised to gather in urban areas to avoid getting caught up in the army offensive.

"They were told to come to town where it is secure. People need to be protected. Cattle keepers must keep to the river," he told Reuters.

Human rights groups say the army has fuelled dissent by committing abuses including rape and torture during its disarmament program among the Murle and Lou Nuer, launched last year.

South Sudan has repeatedly accused Sudan of airdropping weapons and supplies to Yau Yau, who the government says is responsible for a cattle raid that killed over 100 Lou Nuer in February.

Sudan denies the allegations and in turn says South Sudan is supporting rebels on its side of the border.

(Reporting by Hereward Holland; Editing by Louise Ireland and Ulf Laessing)