Details of his plea for forgiveness from his family have emerged after his mother Samia Tabbal, a nuclear scientist, was detained by police in Tripoli.
There have been claims that Tabbal had already told the authorities about his radicalisation.
Adebi’s brother, Hashem and father, Ramadan, have also been arrested.
Officials in Libya have also claimed that the killer only left Libya for England four days before the bombing.
Special Deterrent Force spokesman Ahmed bin Salem said Adebi was giving his “farewell” to his mother by phoning her before the attack, reported the Mirror.
During her arrest, Tabbal was accompanied by her Manchester-born daughter Jomana, 20, who said he acted out of “revenge” for US attacks on Muslim children.
“I think he saw children – Muslim children – dying everywhere, and wanted revenge,” she told the Wall Street Journal.
“He saw the explosives America drops on children in Syria, and he wanted revenge. Whether he got that is between him and God.”
Bin Salem said Libyan investigators believe that Adebi acted alone,bsed on what the family has told them.
Adebi’s brother claimed he had learned to make explosives on the internet and wanted to a “victory for ISIS”.
British police though believe he was part of a terror cell.
British security minister Ben Wallace told the BBC on Friday that police are “confident of rolling up” those responsible for the attack.
Police in Manchester are “confident of rolling up” the suspected terrorist cell behind the attack, according to security minister Ben Wallace.
He said: “This is not a lone individual. We have to close down every lead we find. We have to follow it up and make sure we make the arrests and the searches that we need to do.”