But according to witnesses, he did ask forgiveness for atrocities against civilians committed both by the militants under his command and Ugandan forces.
Dressed in a white shirt, white trousers and black shoes, the elusive Mr Kony emerged from the jungle on Sudan's southern border with the Democratic Republic of Congo (DRC) to give his first news conference in nearly 20 years of war.
"I cannot fight with children. There is not any children in position. There is not any abduction in the LRA," Mr Kony said in broken English.
The Ugandan government and aid groups have accused the LRA of kidnapping thousands of children, forcibly conscripting the boys as soldiers and abusing the girls as sex slaves.
The United Nations children's agency UNICEF says at least 25,000 children have been abducted since the LRA started fighting the army in northern Uganda 19 years ago.
Mr Kony, who describes himself as a mystic and prophet and wishes to introduce a regime based on the Bible's Ten Commandments, blamed a lack "of good communication to the world" for the LRA's appalling reputation.
Breakthrough meetings
But in a meeting earlier with a Ugandan government envoy and Sudanese mediators, Mr Kony begged for forgiveness for the pain caused.
"People were very happy when he asked for forgiveness for the atrocities that the Ugandans (LRA and Ugandan army) committed and the suffering of the people of northern Uganda and southern Sudan," said Betty Achan Ogwalo, a member of the southern Sudan parliament.
As well as the meeting at the trading post of Nabanga on the DRC-Sudan border, Mr Kony attended another one on Saturday with Ugandan peace negotiators and the Sudanese mediators.
The talks are seen as major breakthroughs in peace talks on ending the civil war which are currently under way in the southern Sudanese capital, Juba.
The International Criminal Court (ICC) in The Hague has issued arrest warrants for Mr Kony, his deputy Vincent Otti and three other top commanders, preventing the rebel leader from joining peace talks until now.
But Ugandan President Yoweri Museveni has assured "total amnesty" to Mr Kony if the talks succeed.
Sudan is working with foreign governments to have The Hague's arrest warrants withdrawn in order to enable Mr Kony to negotiate directly with the government.
The United Nations says the war in northern Uganda is one of the world's worst humanitarian disasters and complains that it has largely gone unnoticed by the international community.