The ICC, which was set up in 2002 as the world's first permanent war crimes court, now faces a decision in which it could be accused of bowing to politics if it drops the charges and wrecking peace talks if it does not.
The court confirmed that registry officials had met the LRA delegation on Monday.
The court said in a statement that officials could only discuss procedural issues such as how to file documentation and how to organise defence counsel.
It said: "As a neutral organ that facilitates fair trial, the registry does not engage in substantive discussions with any of the parties on the merits of cases before the court."
Luis Moreno-Ocampo, the ICC prosecutor, has repeatedly said the arrest warrants against the LRA leaders remain valid.
However, last week he said he would not meet the rebels himself but that they could approach the court's judges if they want to challenge his case.
One of the team, David Nyekorach Matsanga told Al Jazeera: "Uganda has got a judicial system that is working. It is not a failed state like Somalia, Liberia or Sierra Leone where you can actually have people taken away from their countries to be charged in The Hague.
"It does not mean that there is only justice in The Hague. Justice can be got in Uganda. Justice is justice," he said in an interview.
Uganda has rejected guaranteeing the LRA immunity to international prosecution until the signing of a final deal, which it wants tied up by March 28 to bring an end to one of Africa's longest-running and most brutal wars.
But it has said it will request that the UN Security Council ask the court to defer its case and the two sides have also agreed to set up special war crimes courts in Uganda.
Matsanga said he hoped the agreements Kony has reached with the Uganda government would help the LRA's case at the court.
He said: "Based on that, we expect the ICC not to continue blocking peace and drop those indictments."
In late February, Uganda and the LRA signed the last in a series of documents paving the way for a final deal to end fighting that has left tens of thousands of people dead and displaced nearly two million people.
Al Jazeera's Mohammed Adow says that since the peace talks have started thousands of displaced people have been leaving camps in Northern Uganda to return home.
Adow said that the success or failure of the peace process now hinges on the decision by the ICC.
A mediator said last week that Kony, whose group is notorious for hacking off body parts and abducting children to fight as soldiers and work as sex slaves, was set to emerge from hiding to sign a final deal.
But it was unclear if he would be prepared to leave the Democratic Republic of Congo, where he is now living, before he receives guarantees over the ICC charges.
Kony has not attended any of the negotiations in Sudan and has not been seen for many months.
The LRA had wanted to rule Uganda according to the Biblical Ten Commandments.