(CNN) -- The Libyan government argued Tuesday that it should not have to hand over Saif al-Islam Gadhafi to the International Criminal Court because the court in the Hague, Netherlands, does not have jurisdiction in the case.
Gadhafi, son of deposed strongman Moammar Gadhafi, was facing an arrest warrant from the ICC for alleged crimes against humanity at the time of his capture in November 2011. The court is still seeking to prosecute him and wants him handed over.
Gadhafi has been held in the Libyan city of Zintan since his capture. The two-day hearing is being held in the Hague.
The ICC has demanded that Libya hand Gadhafi over to face accusations of crimes against humanity. Libya appealed the decision, saying that he should be tried at home.
Court-appointed attorneys Melinda Taylor and Xavier-Jean Keita said in April that Gadhafi has been mistreated and "physically attacked" since his capture.
In a strongly worded statement, the lawyers described Gadhafi as being in a legal black hole, held in total isolation except for visits from officials. He also suffers dental pain because he hasn't had treatment, and Libyan authorities have given him nothing to remedy the pain, the lawyers said.
The Libyan government wants to prosecute Gadhafi itself, as it "regards the trial of Saif al-Islam and Abdullah al-Senussi as a matter of the highest national importance, not only in bringing justice for the Libyan people but also in demonstrating that the new Libyan justice system is capable of conducting fair trials (that meet all applicable international standards) in complex cases."
Al-Senussi, who was Libya's chief of intelligence under Moammar Gadhafi's, is wanted by both the ICC and the Libyan government. He was arrested in Mauritania in March.
The appeal document also seeks to answer ICC concerns about Saif al-Islam Gadhafi's well-being, saying the government "has expended considerable resources in order to ensure the safe and secure temporary custody" of Gadhafi in Zintan and is negotiating to bring him to the capital, where facilities would be better.
Amnesty International has previously called on Libya to hand over Gadhafi.
"An unfair trial before a Libyan court where the accused could face the death penalty is no way to guarantee justice and accountability," the rights group said.
Amnesty has said that Libya does not have a functioning court system and the country was "unable to conduct effective investigations," so "the ICC will be crucial in delivering accountability in Libya."
Libya and the ICC have been going back and forth since his capture about where Saif al-Islam Gadhafi, once his father's heir apparent, will be tried.
Moammar Gadhafi died after his capture by opposition forces a year ago.