Saudi Arabia has charged 11 people over Mr Khashoggi’s death.
Mr Khashoggi entered the Saudi consulate in Turkey on October 2, 2018, and never emerged. His body has never been found.
A UN report said Saudi Arabia bore responsibility for the killing and that the crown prince’s possible role should be investigated.
“This was a heinous crime,” Prince Mohammed, 34, told the programme.
“But I take full responsibility as a leader in Saudi Arabia, especially since it was committed by individuals working for the Saudi government.”
Asked if he ordered the murder of Mr Khashoggi, who had criticised him in columns for The Washington Post, Prince Mohammed replied: “Absolutely not.”
“Some think that I should know what three million people working for the Saudi government do daily,” the crown prince said.
“‘It’s impossible that the three million would send their daily reports to the leader or the second-highest person in the Saudi government.”
In an interview on Thursday, Mr Khashoggi’s fiancee, Hatice Cengiz, told The Associated Press that responsibility for Mr Khashoggi’s killing “was not limited to the perpetrators” and said she wanted Prince Mohammed to tell her: “Why was Jamal killed? Where is his body? What was the motive for this murder?”