Del Ponte has led prosecutions at the court in Arusha since 1999
The United Nation's chief prosecutor for Rwanda and Yugoslavia has been robustly defending her role, as diplomats consider calls for her job to be split in two.
The UN Secretary General, Kofi Annan, has recommended Carla Del Ponte heads the Yugoslav tribunal for another four years but is removed from the Rwanda court.
He argues the job is too big for one person, and most Security Council members agree the courts could be run more efficiently.
Ms Del Ponte has complained to the Security Council she was a victim of political pressure from Rwanda, and said international justice could be damaged if her duties are shifted.
Rwandans have long argued that the International Criminal Tribunal in Arusha, Tanzania, - examining the genocide of 1994 - has been plagued by mismanagement and a lack of attention from successive prosecutors.
Gerald Gahima, Rwanda's Prosecutor General, said people took "strong exception" to the fact that the investigation of more than one million deaths has been made a "part-time job of a prosecutor based on another continent".
She and some human rights groups believe the predominantly Tutsi government may be trying to push her out because she proposed investigating the
Tutsi-led Rwandan Patriotic Army for the suspected reprisal killings of more than 30,000 Hutus.
The Swiss judge, who took up the job in 1999, does have some support on the Security Council.
"No government, and particularly not the Rwanda Government, should have any interference in the work of the tribunal and in the independence of the prosecutor," said Mexican Ambassador Adolfo Aguilar Zinser.
However, he said Mexico would back the council's consensus, which is thought to favour the secretary general's proposals.
The moves come as her dual mandate comes up for
renewal on 15 September.