The duo made the plea during an interview with the CNN on Sunday.
"All what we want right now is to bury him in Al-Baqi (cemetery) in Medina (Saudi Arabia) with the rest of his family," said 35-year-old Salah, the eldest of Khashoggi’s offspring, two sons and two daughters.
"I talked about that with the Saudi authorities and I just hope that it happens soon," he added.
Khashoggi was a US citizen and The Washington Post
columnist, who would openly critique the kingdom, especially Crown Prince Mohammad bin Salman.
He entered the diplomatic mission to obtain documents for a pending marriage, but never left the premises. Saudi authorities were for long in denial about his fate before they said he had been murdered during a “rogue” operation.
"I really hope that whatever happened wasn't painful for him, or it was quick. Or he had a peaceful death," said Abdullah, 33.
"Jamal was a moderate person. He was liked by everybody. He had differences and common values with everyone," Salah added, calling him an "amazing" father.
They also described Khashoggi as "courageous, generous, and very brave."
Turkey says his murder was ordered at the top echelons of the Saudi royal family, and that he was dismembered afterwards.
Addressing the circumstances surrounding the case, Salah said, "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."
"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," Abdullah said.
"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," he added.
Separately, Reuters reported that King Salman would be embarking on a week-long domestic tour on Tuesday, amid the political crisis ensuing Khashoggi’s death.
The trip would be the first one by the monarch since he ascended the throne three years ago.
Local media reported expected stops in the provinces of Qassim and Hail, both northwest of Riyadh, and pending launches of health, education and infrastructure projects during the tour.