Mrs O'Brien revealed that she sympathized with Rwanda's demands to take on the remaining cases at ICTR after its completion, but the decision on the transfers rested in the hands of Security Council and ICTR judges, reported Tuesday New Times of Rwanda.
The ICTR is set to wind up its all first instance trials by end of the year and appeals by 2010.
Mrs O'Brien expressed this after Monday's meeting with Rwanda's Prosecutor General, Martin Ngoga, over ICTR's residual mechanisms.
She however expressed optimism that a final stand will be reached, adding that the UN appreciated and was supportive of Rwanda's continuous efforts to discuss the issue of residual mechanisms and the legacy of the Tanzania-based tribunal.
Rwanda has made its intentions clear that it wants the untried suspects to be transferred to Rwanda to stand trial and convicts brought in the country to serve their respective sentences.
However, Rwanda's applications to do so have been turned down by the UN tribunal on the grounds that the suspects might not get a fair hearing.
Last year, ICTR Chief Prosecutor Hassan Bubacar Jallow moved a motion to have five suspects, four of whom are in the tribunal's custody, transferred to Rwanda but was turned down by the judges.
Ngoga reiterated that Rwanda was interested to have the untried cases transferred to Kigali when the Tribunal ends its mandate.
The ICTR was established by the UN Security Council in 1994 to try masterminds of genocide against mainly ethnic Tutsis and moderate Hutus.
Mrs O'Brien who also visited Kenya to discuss with the authorities there about the issue of Kenya failing to apprehend one of the most wanted fugitives, Felicien Kabuga, said that she was optimistic that concrete steps will be taken to address the issue.
On Thursday last week, the UN Legal chief held talks with top authorities of ICTR in Arusha, Tanzania before flying out to Nairobi on Friday.
© Hirondelle News Agency