Annan said Wednesday that Cameroon's Paul Biya and Olusegun Obasanjo of Nigeria will focus on securing a delayed Nigerian troop withdrawal and working out the maritime frontier, the two main hurdles in fully resolving the dispute over the Bakassi peninsula.
"The heads of state agreed this morning that the process should be expedited and we should work out the new direction of the maritime border," Annan told journalists.
"We also agreed that the new programme of withdrawal of the Nigerian troops would be worked out and agreed upon by the two presidents and myself," he added.
Annan pledged to remain personally engaged in the process, while the United Nations would be involved in monitoring and verifying an eventual withdrawal of Nigerian troops once the two leaders and the UN work out a timetable.
Nigeria was scheduled to pull out a military contingent from Bakassi last September but this was postponed indefinitely.
Annan praised progress in the region around the disputed peninsula, especially a "smooth transfer of authority along the land border" over the past year.
Last month, the two countries overcame a disagreement on a section of their land border which had held up an attempt to begin re-marking the disputed frontier.
Their move followed a protest by the United Nations, after Nigeria stalled a survey by a commission of officials from Nigeria, Cameroon and the UN seeking sites for new border markers.
The dispute over the course of Nigeria and Cameroon's 1,690 kilometre (1,065 mile) border -- which was drawn by their former colonial rulers -- had fuelled occasional skirmishes between the countries' forces.
Cameroon took the matter to the International Court of Justice in The Hague, which in October 2002 issued a ruling defining the border and handing the potentially oil-rich Bakassi Peninsula to Cameroon.
Nigeria has pledged to abide by the ruling under a UN-supervised process but its forces have missed several deadlines to pull out of Bakassi.
Biya said he was confident that the process was heading in the right direction, especially with the decision to press ahead with the border issue.
"That also means everyone including Nigeria recognises the sovereignty of Cameroon as defined by previous treaties and especially the ruling in The Hague," the Cameroon president told journalists.
"I think we have made a step forward... and we are heading to a definite solution to the problem," he added.
Obasanjo's spokeswoman Oluremi Oyo quoted him as saying that the manner in which the two countries tried to resolve their boundary problem has been "exemplary and worthy of emulation".
He expressed the belief that it will move forward the process of demarcation, adding that the human aspect of the problem is paramount and should not be treated with levity.
Bakassi is a 1,000 square kilometre (400 sq mile) patch of coastal swamp with fishing grounds and potentially rich oil fields reaching into the Gulf Guinea.