He said that his son visited Libya a month-and-a -half ago.
Abedi Sr said: 'We don't believe in killing innocents. This is not us.'
He said his other son, Ismail, was arrested in England on Tuesday morning.
He said Salman was planning to head from Saudi Arabia to Libya to spend the holy month of Ramadan with family.
Abedi fled Tripoli in 1993 after Moammar Gadhafi's security authorities issued an arrest warrant and eventually sought political asylum in Britain.
Now, he is the administrative manager of the Central Security force in Tripoli.
It is understood that Abedi was ‘known’ to the Security Services through his associations to those linked to terrorism in Manchester’s Libyan community.
These are said to have included 24 year-old Abdalraouf Abdallah, who was jailed for nine years after being convicted of preparing acts of terrorism and funding terrorism.
Abdallah, who is partially paralysed after being shot during the Libyan Revolution, is said to have helped men travel to Syria to fight.
Inquiries led officials at the time to believe Abedi was not of significance to that operation.
His family was also ‘known’ through his father’s one time association with an Al Qaeda-linked group.
A former Libyan security official says the father of the alleged Manchester arena bomber was allegedly member of a former Al-Qaeda-backed group in Libya.
Former Libyan security official Abdel-Basit Haroun said Wednesday he personally knew Ramadan Abedi, the father of Salman Abedi, and that the elder Abedi was a member of the Libyan Islamic Fighting group in the 1990s.
The group had links to Al-Qaeda.
Although the LIFG disbanded, Haroun says the father belongs to the Salafi Jihadi movement, the most extreme sect of Salafism and from which Al-Qaeda and the Islamic State group hail.
Haroun says Abedi, also known as Abu Ismail, had returned to the Libyan capital of Tripoli.
