The International Court of Justice has been requested by Belgium to extradite former Chadian President Hissene Habre.
Mr Habre denies accusation he committed crimes against humanities during his reign.
He is alleged to have killed and tortured tens of thousands of opposition activists between 1982 and 1990.
He has been living in Senegal since his ouster in 1990 and was arrested in 2005, however Senegalese authorities have refused four previous extradition requests by the Belgian government.
Belgium has now asked the ICJ to order Senegal to fulfil its international obligations and either prosecute Mr Habre or extradite him so he can stand trial in Brussels.
The case is about "taking a stand against impunity in the most serious crimes in international law", Belgian representative Paul Rietjens said during the opening remarks of the hearing in The Hague, the Associated Press reports.
A Chadian court sentenced Mr Habre to death in absentia in 2008, with Senegal planning to extradite him to his native country in 2011.
However, pleas by the UN and human rights groups put an end to the plans, as there were fears Mr Habre could be tortured on his return.
Belgium’s universal jurisdiction law allows victims to file complaints and judges to prosecute human rights offences committed anywhere in the world.
