Libyan authorities have detained the alleged suicide bomber's father as well as a brother.
"We are working closely and intensively with our British partners to probe possible terrorist networks and we have achieved important progress," deputy interior minister Abdelsalam Ashour told reporters.
Britain has named the suspected suicide bomber who killed 22 people in an attack on a Manchester concert Monday as Salman Abedi, who was born in Britain of Libyan origin.
Ashour, a member of the UN-backed Government of National Accord (GNA), said the interior ministry's Deterrence Force was in charge of the investigation but gave no further details.
"We have strong and close ties with our (British) friends," he told reporters, reading from a statement.
Libyan authorities have detained the alleged suicide bomber's father as well as a brother, sources in Libya have said.
Investigators in Britain were trying to track down a jihadist network suspected of having orchestrated the attack which also wounded dozens.
After arresting a 23-year-old man on Tuesday, British police said they had taken three more men into custody on Wednesday in south Manchester, where Abedi lived.
Monday's attack was claimed by the Islamic State group.