"Everybody's telling a different story. I'm trying to simplify it as much as possible. He died," Abdullah Khashoggi said. "It's not a normal situation and not a normal death."
"I really hope that whatever happened wasn't painful for him, or it was quick," he added.
Salah Khashoggi, who lives in Saudi Arabia, became the public face of the family's sorrow when a photograph of him, stone-faced, meeting Saudi King Salman and Crown Prince Mohammed bin Salman was shared on social media and interpreted as evidence of the family's rage at the royal family.
But in fact, Salah Khashoggi said, the king had assured him that "everybody involved will be brought to justice" for the killing.
"I have faith in that. This will happen," he said.
Erdogan has said that Jamal Khashoggi's killing by Saudi agents was premeditated and that the order came from the "highest levels" of the Saudi government, although he has not specified who he thinks was responsible. Erdogan also has demanded that the Saudi government reveal the location of Khashoggi's body.
Turkey has said that a hit squad sent from Saudi Arabia strangled Khashoggi shortly after he entered the consulate to seek a document he needed for his planned marriage to his Turkish fiancee. Turkish authorities said the team dismembered Khashoggi's body and disposed of it.
Turkey has repeatedly accused Saudi authorities of trying to obstruct its investigation. On Monday, a Turkish official said that at least two members of a team that Saudi Arabia sent to investigate Khashoggi's killing were actually there to cover it up.
The official, who was not authorised to comment on the record and spoke on the condition of anonymity, said the dispatch of the two men to Turkey "suggests that Khashoggi's slaying was within the knowledge of top Saudi officials."
The official confirmed details in a report published Monday in Turkey's pro-government Sabah newspaper that said the two men - a chemist and toxicologist - were part of a delegation of Saudi investigators sent to Turkey nine days after Khashoggi was killed.
Beginning October 12, the two men visited the consulate regularly for a week, the paper reported.
"We believe that the two individuals came to Turkey for the sole purpose of covering up evidence," the official said.