The officials hoped the move would help to boost efforts to end a two-decade conflict and to speed up peace talks that resumed last week.
The LRA's senior commanders have repeatedly said they will never sign a peace deal until The Hague-based ICC drops its indictments against them.
The LRA walked out of peace talks nearly a month ago, accusing the army of violating an August truce by attacking their fighters in southern Sudan.
Walter Ochora, the government district commissioner for Gulu, which was at the centre of Uganda's 20-year war, told reporters in Kampala that Kony had said he would be willing to face justice for war crimes in Uganda.
Ochora quoted Kony as saying: "We are ready for accountability in Uganda where we can put our case and the government put their case.
"We shall talk freely and disclose all."
LRA officials were not immediately available for comment.
Local politicians in the war-torn north have advocated traditional justice for the LRA leaders, who are accused of killing civilians, rape, torture, mutilation and abducting children to swell their ranks.
"According to Kony, the ICC has been prejudiced and has not given him a hearing because he is not in power.
"It is the weak facing justice while the powerful are left unmolested."
A government-appointed lawyer who joined the delegation to consult Kony on the implications of the ICC indictments said he noticed a shift in tone, with the LRA leaders relaxing earlier demands that the indictments be scrapped.
Owiny-Dollo said: "This time round, I could see they had come to terms with the fact that they could not wish the ICC away."