JUBA, Sudan, July 5 (Reuters) - Uganda's fugitive rebel leader Joseph Kony has made contact with the U.N. envoy for northern Uganda's conflict and told him he is committed to signing a final peace deal to end 20 years of war.

Two years of peace talks between Kampala and Kony's Lord's Resistance Army (LRA) broke down in April prompting Uganda, Sudan and Congo to threaten a joint military offensive against the guerrillas, who are now based in northeastern Congo.

U.N. envoy Joachim Chissano told reporters in south Sudan's capital Juba on Saturday that he had spoken to the elusive rebel chief by satellite telephone. He said Kony wanted another meeting on the remote Sudan-Congo border.

"He promised to conclude the process ... this (meeting) is a step towards a conclusion," Chissano said. He did not give further details.

Addressing the same news conference, the chief mediator for the talks, south Sudan's Vice-President Riek Machar, said no date had been set yet for the meeting.

Delegates from the LRA and the Ugandan government agreed on a final deal earlier this year. But Kony, who is wanted by the International Criminal Court in The Hague, failed to turn up for an April signing ceremony.

"We will meet and we hope he signs," Machar said. "If Joseph Kony has other issues to discuss, we'll discuss with him."

Uganda's two-decade civil war uprooted 2 million people and destabilised neighbouring parts of oil-producing south Sudan and mineral-rich eastern Democratic Republic of Congo.

At an African Union summit in Egypt on Monday, the top U.S. diplomat for Africa warned that Kony was re-arming, and said the United Nations should boost its peacekeeping force in Congo to contain or catch him. (Reporting by Skye Wheeler; Writing by Daniel Wallis; editing by Ralph Boulton) (For full Reuters Africa coverage and to have your say on the top issues, visit: http://africa.reuters.com/)