Their reaffirmation came in recognition of the "deteriorating security and humanitarian situation" in the northeastern district of Ituri in the DRC, where Uganda still has troops.
The accord provides for the total withdrawal of Ugandan troops from the DRC and the normalisation of relations between Kinshasa and Kampala.
Kabila and Museveni ended their talks as their foreign ministers signed an amendment to the Luanda accord, allowing for a new timetable for the work of the envisioned Ituri Pacification Commission (IPC).
Under the new timetable, the IPC should have been established and begun operating by 17 February. It should end its work on 20 March, by which date Ugandan troops should have completed their withdrawal from the DRC. The amendment also creates a permanent consultative mechanism to enable the presidents to monitor the situation in Ituri closely and take "appropriate action to help them maintain a climate of peace and security in the region".
In their joint communique, the leaders said they had agreed that the IPC's preparatory committee be composed of two representatives each from the governments of the DRC and Uganda and the UN Mission in the DRC, and four from the stakeholders in Ituri.
The presidents also jointly condemned those who continued to supply weapons to armed factions in Ituri, resulting in the escalation of violence and human suffering.
Museveni, who acknowledged the continuing presence of 2,000 Ugandan troops in the DRC, said he and his DRC counterpart would persevere in their efforts to achieve peace.
"We shall not grow tired," Museveni said. "The formation of the Ituri Pacification Committee is just one step. But the most important thing is to have one government in the Democratic Republic of the Congo."
Kabila said he was "optimistic" that, this time, the Ugandan troops would withdraw fully, and described the establishment of the IPC as "a positive development".
According to the UN panel of experts on the illegal exploitation of DRC resources, some 3.5 million people have died since 1998, when Ugandan troops entered the DRC's civil war on the side of rebels opposed to the Kinshasa government.
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