Judges at the International Criminal Court (ICC) based in The Hague said Libya must extradite Senussi over his alleged role in orchestrating reprisals against protesters in the 2011 uprising that overthrew Gaddafi.
However, Libya's leadership claims it has the ability to ensure a fair trial at home.
The court could refer the case to the UN Security Council if the North African state continues to block it.
Ahmed al Jehani, the Libyan lawyer who liaises between the Government in Tripoli and the ICC, said Libya would continue to push for its right to judge Senussi – who has also been linked to the 1988 bombing of Pan Am Flight 103 over Lockerbie that killed 270 people.
Mr Jehani added: "We completed the appeal to the ICC after the order to hand him over. Libya continues in this appeal process to prove it wants to be part of the international community. The old Libya would not have bothered."
Last week, ICC judges ordered Libya to hand over Senussi and let him see his lawyer, raising the stakes in a dispute over who has the right to try the deposed strongman's top lieutenants. Libya has become a test case of the effectiveness of the 10-year-old court, which relies on the co-operation of member states to arrest suspects and enforce its orders.
Mr Jehani said Senussi has requested to be tried by the ICC and has not yet had access to his British lawyer, Ben Emmerson.
Senussi was arrested early last year after arriving with a false Malian passport on a flight to the Mauritanian capital, Nouakchott, from Morocco.
Allegations recently surfaced that Libya paid Mauritania $200 million (£125m) to ignore the ICC arrest warrant last year, sending Senussi to Tripoli rather than to the detention centre in The Hague.
Diplomatic sources said the US was keen to question him about Lockerbie.
Libya's new rulers, who aim to draw up a democratic constitution this year, are keen to try Gaddafi's family members and loyalists at home to show the country's citizens that those who helped Gaddafi stay in power for 42 years are being punished.
Human rights activists worry a weak central government and a relative lack of rule of law mean legal proceedings – both for Senussi and for Gaddafi's son Saif al Islam – will not meet international standards.
Mr Jehani said no date had been set for Senussi or Saif al Islam to go to trial because the prosecutor-general has yet to decide on a proposal to try high-level Gaddafi government officials in one proceeding.
"He is still studying this option with the minister of justice and others so we don't know when it will be held," added Mr Jehani
Senussi's 20-year-old daughter, who also is in custody in Libya, was granted a visit to see her father yesterday, said Justice Minister Salah al Marghani. Al Unood Senussi, who is also a niece of Gaddafi's wife, Safiah, was detained by the military police in October, accused of entering Libya illegally.