Uganda’s President Yoweri Museveni made the pledge, disregarding arrest warrants from the International Criminal Court.
Mr Museveni criticised the United Nations for failing to arrest the rebel chief when he was hiding in the Democratic Republic of Congo, after fleeing his base in southern Sudan.
The ICC responded by reminding Uganda of its obligation to hand Mr Kony over under the Treaty of Rome, which it has signed and ratified.
Delegates from both Uganada and the LRA are in the Sudanese city of Juba preparing for peace talks to be mediated by the semi-autonomous government of southern Sudan
The talks are aimed at ending more than two decades of fighting in northern Uganda and southern Sudan.
Several attempts to broker an end to the insurgency have failed. ICC war crimes indictments issued against Mr Kony and four top lieutenants initially cast doubt over the latest effort.
Mr Museveni claimed that the ICC had lost the moral authority to try Mr Kony.
Mr Museveni said the UN failed to arrest him even when his fighters were suspected of killing at least eight UN peacekeepers in DRC, where they had fled to escape the Ugandan army.
Tens of thousands of people have been killed and about two million displaced in northern Uganda since the LRA took control of a regional rebellion in 1988 in a bid to oust Mr Museveni.
It led to what the UN and other humanitarian groups have described as the world's most brutal and forgotten conflict.
A self-styled prophet and mystic, Mr Kony is among the world's most wanted men and is the subject of international arrest notices from Interpol.
In a rare media interview released last week, Kony denied he was a terrorist, describing himself as a freedom fighter, fighting for freedom in Uganda.