Biden said on Friday he told Prince Mohammed he held him responsible for the 2018 murder of Washington Post journalist Khashoggi at the Saudi consulate in Istanbul, shortly after exchanging a fist bump with the kingdom's de facto ruler.
"The President raised the issue... And the crown prince responded that this was a painful episode for Saudi Arabia and that it was a terrible mistake," the kingdom's Minister of State for Foreign Affairs Adel al-Jubeir said.
Those who were accused were brought to trial and punished with prison terms, he said.
US intelligence agencies believe the crown prince ordered Khashoggi's killing, which he denies.
Jubeir, talking to Reuters about Friday's conversation between the two leaders, said the crown prince had made the case that trying to impose values by force on other countries could backfire.
"It has not worked when the US tried to impose values on Afghanistan and Iraq. In fact, it backfired. It does not work when people try to impose values by force on other countries," Jubeir quoted the prince, known as MbS, as telling Biden.
"Countries have different values and those values should be respected," MbS told Biden.
The exchange highlighted the tensions that have weighed on the relationship between Washington and Riyadh, its closest Arab ally, over several issues, including Khashoggi, high oil prices and the Yemen war.
Biden, who landed in Saudi Arabia on Friday in his first Middle East trip as president, held a summit on Saturday with six Gulf states and Egypt, Jordan and Iraq while downplaying his meeting with Prince Mohammed. That encounter has drawn criticism at home over human rights abuses.
Biden had promised to make Saudi Arabia a "pariah" on the global stage over the 2018 murder of Khashoggi, but ultimately decided US interests dictated improving relations with the world's top oil exporter and Arab powerhouse.
After the summit, the leaders gathered for a group picture at which Biden kept his distance from Prince Mohammed.
"His Royal Highness mentioned to the President that mistakes like this happen in other countries and we saw a mistake like this being committed by the United States in Abu Ghraib (prison in Iraq)," Jubeir said.
Prince Mohammed also raised the killing of Palestinian-American journalist Shireen Abu Akleh during an Israeli raid in the West Bank.
Abu Akleh, who worked for the Al Jazeera network, was shot in the head on May 11 while reporting on an Israeli raid in the occupied West Bank city of Jenin.
Palestinians believe she was killed deliberately by Israeli troops. Israel denies its soldiers shot her on purpose, and say she may have been killed either by errant army fire or a shot fired by a Palestinian gunman.
Jubeir rejected the accusation that Saudi Arabia has hundreds of political prisoners.
"That's absolutely not correct. We have prisoners in Saudi Arabia who have committed crimes and who were put to trial by our courts and were found guilty," he said.
"The notion that they would be described as political prisoners is ridiculous," he added.
Washington has softened its stance on Saudi Arabia since Russia invaded Ukraine earlier this year, triggering one of the world's worst energy supply crises.