Speaking at a business forum in Riyadh, Mohammed bin Salman said “the crime was painful to all Saudis” but he would never allow any rift with Turkey.
The Saudis have previously denied accusations that the prince, the de facto ruler, had a role in the killing.
Khashoggi died during a 2 October visit to the Saudi consulate in Istanbul.
The Saudi government has blamed the murder on “rogue agents”.
Turkish President Recep Tayyip Erdogan says the journalist, a prominent critic of the government, was the victim of a carefully planned “political murder” by Saudi intelligence officers and other officials.
What did the crown prince say?
These were his first public comments since the Saudis admitted Khashoggi had been killed at the consulate.
He said the killing was “a heinous crime that cannot be justified” and vowed that “those behind this crime will be held accountable… in the end justice will prevail”.
He said there had been good co-operation with Turkey, adding: “A lot of people are trying to seize this painful situation to create a rift between Saudi Arabia and Turkey. And I want to send them a message: you will never be able to do that.
“The rift will never be there.”
The three-day conference, called the Future Investment Initiative but dubbed “Davos in the desert” after the Swiss forum, is important for the Saudis but has already been boycotted by many Western business leaders and politicians.
The Saudis have tried to portray business as usual at the forum, although Energy Minister Khalid al-Falih acknowledged on Tuesday there was a “crisis” over the Khashoggi issue.
On Tuesday the crown prince joined his father, King Salman, in meeting members of the Khashoggi family.
The crown prince, 33, is considered the de facto ruler of the world’s leading oil exporter. He has won some plaudits for reform, but also heavy criticism for the handling of Yemen and Qatar – and even calls to be replaced after the Khashoggi affair, amid suspicion of how much he was involved.