The Tribunal has been tasked to try key suspects of April-July 1994 Rwanda genocide, which according to UN estimates, claimed lives of about 800,000 ethnic Tutsis and moderate Hutus.
The UN Security Council has insisted that the ICTR completed all first instance trials by the end of December.
Mrs. O' Brien held talks Wednesday with ICTR President, Justice Dennis Byron, Prosecutor Justice Hassan Bubacar Jallow, and the Registrar, Adama Dieng, according to the Tribunal's spokesperson Roland Amoussouga.
She also met with judges.
On Thursday, she will meet ICTR staff and visit the Special ICTR detention centre on the outskirts of Arusha town, before winding up her visit with a meeting with ICTR's "coordination committee" made up of President, Prosecutor and Registrar.
The UN legal counsel will visit on Friday Nairobi and fly on Monday to Kigali.
In Kenya, she will discuss with the authorities on "questions of co-operation with the ICTR", according to Amoussouga.
The ICTR claims that the Kenyan government was not doing enough to arrest billionaire Felicien Kabuga, alleged financier of the 1994 genocide, who is believed to be hiding in the East African country.
In Rwanda, the discussions are expected to revolve around the Tribunal's archives and on the relocation of convicted persons.
The Rwandan government, which has until now requested in vain to receive ICTR prisoners, will have an added voice following the signing last week of an agreement to receive convicts from the Special Court for Sierra Leone (SCSL) created, as the Arusha one, by the UN Security Council.
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© Hirondelle News Agency