In a statement, the UN Secretary General's Special Representative, Legwaila Joseph Legwaila, said talks of "common concern" were underway about what security measures would be in place for demarcation - now scheduled for July.
The security talks have been taking place between both countries, the independent Eritrea-Ethiopia Boundary Commission (EEBC) and the UN's Mission in Ethiopia and Eritrea (UNMEE).
Issues under discussion included who would be responsible for securing the pillar sites and for providing security to EEBC staff.
Legwaila's statement comes after the EEBC urged UNMEE to ensure the safety of boundary commission staff who will be working on the ground in the 25 km-wide buffer zone to mark out the border.
The commission has also asked UNMEE to protect the concrete pillars that will mark the new 1,000 km-long border to ensure the bases "are not disturbed".
But in his statement, Legwaila said it was felt that Ethiopia and Eritrea should take responsibility for security during demarcation, while UNMEE "could assist the process".
"UNMEE, already present in many areas on the ground, could assist the process by monitoring the parties' discharge of this responsibility within the context of its monitoring mandate and without leading to a confusing duplication of functions on the ground," he stated.
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