By Will Ross
BBC News, Kampala
The United Nations says it has held a meeting with a group of the Ugandan rebels, the Lord's Resistance Army (LRA), for the first time.
Uganda's peace process is extremely fragile
A senior member of the Congolese army also met the Ugandan rebels, and called for them to disarm.
The LRA has been fighting a war with no clear agenda for the past 19 years.
The rebels normally operate in northern Uganda and southern Sudan, but last week some LRA rebels crossed into the Democratic Republic of Congo.
A UN official said at the meeting, in the north-east of the Democratic Republic of Congo, that the Ugandan rebels must disarm before their future status could be discussed.
The official said UN officials and a senior commander of the Congolese national army, General Paderi, met the LRA rebels for over three hours, and that discussions were continuing by telephone.
This group of LRA rebels walked from southern Sudan across the border into the north-east of DR Congo last week, a move which took many people by surprise.
The LRA's deputy commander is believed to be among them, although he did not attend Sunday's meeting.
Even if this group of rebels agrees to disarm, the end of the war in northern Uganda will be far from guaranteed.
LRA commander Joseph Kony remains with his fighters in southern Sudan.
It is somewhat surprising that this first meeting between the elusive LRA rebels, the UN and the Congolese army, was apparently easy to arrange.
Previous efforts between the LRA and the Ugandan government to talk peace have broken down with both sides being accused of not showing enough commitment to end the 19 years of war.