A visibly emotional Abdullah Khashoggi said he hoped the death of his “courageous, generous and very brave” father was “quick”.
Speaking after weeks of anguish, the 33-year-old said: “I really hope that whatever happened wasn’t painful for him, or it was quick. Or he had a peaceful death.”
The journalist’s older son Salah Khashoggi also called on the Saudi authorities to return the body of their father so his family can properly grieve.
He told US TV network CNN: “All what we want right now is to bury him in Al-Baqi cemetery in Medina, Saudi Arabia, with the rest of his family.
“I talked about that with the Saudi authorities and I just hope that it happens soon.”
Mr Khashoggi, 57, vanished on October 2 after entering the Saudi Arabia Consulate, sparking a man hunt.
Parts of his body, including his face, were found in in the Saudi Consul general’s garden located 500 metres away from the consulate building in Turkey.
The Saudis have been forced to admit that the death of Mr Khashoggi was “premeditated” after pressure continued to mount from Turkish officials who claim that they have audio and visual recordings of the journalist being strangled, dismembered and, allegedly, dissolved in acid by a Saudi hit squad.
Salah spoke of the “burden” of not knowing what happened to their father.
“Our source is the same source that you have. It is a mystery. This is putting a lot of burden on us, all of us. That everybody is seeking for information just as we do. They think that we have answers, and unfortunately we don’t.”
Abdullah added: “It’s difficult, it’s not easy. Especially when the story gets this big. It’s not easy, it’s confusing. Even the way we grieve, it’s a bit confusing.
“At the same time, we’re looking at the media and the misinformation. There’s a lot of ups and downs. We’re trying to be emotional and at the same time we’re trying to get the story – bits and pieces of the story to complete the whole picture.
“It’s confusing and difficult. It’s not a normal situation and not a normal death.”
Their emotional appeal comes after Saudi state media released pictures taken of Salah meeting and shaking hands with Crown Prince Mohammed bin Salman, who has been blamed for the crime.
He also met Saudi Arabia’s King Salman bin Abdelaziz.
But Salah said the exchange had been misinterpreted.
He said: “I mean there was nothing, they were just over analyzing the whole situation.
“I understand why they’re trying to do that. They’re trying to get as much information as they can out of anything, which is something that we’re also doing. Sometimes they’re just baseless claims, sometimes they just don’t make any sense.”
The crown prince has said the murder was “heinous and cannot be justified” after appearing on television two days after body parts were found.
Mr Khashoggi was a Washington Post contributor and critic of the Saudi regime.
His death has brought waves of scrutiny on Saudi Arabia and the Crown Prince, who Mr Khashoggi has personally criticised in the past.