The father of the man suspected to have perpetrated the fatal shootings of four Marines in Chattanooga, Tennessee is a native of the Palestinian territories who was once questioned by US authorities over alleged ties to Islamic terrorists, NBC News is reporting on Friday.US authorities are investigating travel to the Middle East by the suspect, Mohammod Youssuf Abdulazeez, including at least one trip to Jordan and possibly one to Yemen, a source close to the probe said on Friday.Abdulazeez, 24, who the FBI identified as the shooter, was shot to death in a rampage on Thursday at two military facilities in Chattanooga.The suspect, seen driving an open-top Ford Mustang, sprayed gunfire at a joint military recruiting center in a strip mall, riddling the glass facade with bullet holes, then drove to a Naval Reserve Center about 6 miles (10 km) away, where he killed the four Marines before he died in a firefight with police.The shooting, which comes at a time when US military and law enforcement authorities are increasingly concerned about the threat "lone wolves" pose to domestic targets, also injured three people, including a sailor who was critically wounded.Investigators are trying to determine whether the suspect had any contact with militants or militant groups but have no evidence so far that he did, the US government source told Reuters.US law enforcement officials said they were investigating whether he was inspired by Islamic State or similar extremists.Islamic State had threatened to step up violence in the holy fasting month of Ramadan, which ends on Friday evening.The group, also known as ISIS and ISIL, claimed responsibility after a gunman killed 37 tourists in Tunisia in June, the same day as an attack in France and a suicide bombing in Kuwait.The SITE Intelligence Group, which tracks extremist groups, said Abdulazeez blogged on Monday "life is short and bitter" and that Muslims should not miss an opportunity to "submit to Allah." Reuters could not independently verify the postings.While investigators still have no specific evidence of what might have prompted the suspect to carry out the shooting, they believe family or psychological issues may have contributed, according to the source, who was not authorized to speak on the record.His father, Youssuf Abdulazeez, who attended Texas A&M University, according to his Facebook page, appears to be a high achiever. He works for Chattanooga's Department of Public Works as a soil engineering expert, according to local media reports citing city records.The suspect appears to have followed in his father's footsteps. According to a resume believed to have been posted online by Abdulazeez, he attended high school in a Chattanooga suburb and graduated from the University of Tennessee in 2012 with an engineering degree. His work experience includes an internship with the Tennessee Valley Authority, a regional power utility.Years ago, the father came under investigation by a Joint Terrorism Task Force for possible connections to a militant group, the source said, but he was cleared of any association with terrorism or wrongdoing. It is possible but not certain that the probe resulted in the father's name being placed on a terrorist watch list, according to the source.