The 47-year-old has previously denied involvement in terrorism, claiming to be a charity worker. He also claimed to be a journalist at one point.
He is already wanted by the US, Interpol, Libya and the UN. Here he is constantly monitored by the Middle Eastern section of the Special Branch but he has never faced any terror charges.
Buwisir, in Ireland since 1982, lives at his family home in Broadford Drive, Ballinteer, with his wife and children.
Questions have been raised on how he has been able to maintain Irish Citizenship, which was granted by the Department of Foreign Affairs.