(updates with quotes, background, details) By Tim Cocks KAMPALA, Dec 11 (Reuters) - Ugandan President Yoweri Museveni held direct talks over the phone with the top command of the Lord's Resistance Army for the first time since their 20-year insurgency began, the rebels said on Monday. In what a rebel representative called "a significant step in confidence building," Museveni had a 30-minute conversation with LRA deputy Vincent Otti on Sunday in which he heard complaints about the army besieging the rebels despite peace talks. "It is the first time. It shows the LRA are serious about peace," Martin Ojul, head of the delegates representing the LRA at negotiations in south Sudan, told Reuters by satellite phone from the LRA leaders' hideout. Ojul said he was present with Otti for the conversation. Presidential press secretary Tamale Mirundi said he could not comment on Museveni's private conversations. "The president has said he is willing to talk to the LRA leadership. I wouldn't be surprised," he told Reuters. Uganda's stop-start peace talks -- aiming to end a conflict that has killed thousands and displaced 1.7 million -- stalled last week when the LRA delegates walked out. They accused the army of ambushing their fighters in south Sudan, killing three. A landmark truce renewed last month gave the rebels until December to assemble in two places in south Sudan. But the rebels said the army attacked them as they tried to reach a meeting point east of the Nile. Independent monitors found both sides violated the truce when they clashed -- the army by firing at the LRA, the LRA by wandering in a part of south Sudan that was out of bounds, hundreds of miles from the agreed assembly area. Ojul said Otti had complained to Museveni about the Ugandan army's presence in south Sudan and Museveni had agreed to withdraw troops from the Juba-Torit road, near where the clashes took place. "He (Otti) told him we can't assemble because the UPDF (Uganda People's Defence Forces) were tracking us left and right. He said he'd tell his troops to withdraw from there," Ojul said. Some fear the LRA will never sign a peace deal until the International Criminal Court (ICC) in the Hague drops indictments against its top commanders. Kony, Otti and three others are wanted for war crimes such as killing civilians, slicing body parts off victims and kidnapping children to use as fighters and sex-slaves. Uganda says it might request the ICC to drop the charges if the LRA sign a peace deal. "People are trying to intimidate them, saying he will hand them to the ICC," Mirundi said. "The president has offered his word that he will not if they come out voluntarily." Meanwhile, local press reported that LRA leader Joseph Kony was reunited with his mother, whom the Ugandan government helped transport to his forest hideout on his request, on Sunday, for the first time since he led his uprising in 1986.