Saudi journalist Jamal Khashoggi, a columnist for The Washington Post newspaper, who apparently went missing after going to the Saudi Consulate in Istanbul.
During Friday's rally, many US officials, including his allies in Congress, took a harder stance on the Saudi investigation.
The announcement comes as pressure mounted on Prince Mohammed bin Salman to investigate the death of one of his most prominent Saudi critics.
The Saudi government has released an explanation of how they believe journalist Jamal Khashoggi died at the Saudi consulate in Istanbul, Turkey.
Guterres "stresses the need for a prompt, thorough and transparent investigation into the circumstances of Mr. Khashoggi's death and full accountability for those responsible", spokesman Stephane Dujarric said in a statement.
Even as legislators from across the political spectrum in Washington expressed scepticism over the Saudi narrative, Trump on Friday said Riyadh's explanation was credible and called the arrests a "good first step". "I do." But he said before he decided what to do next, he wanted to talk to the crown prince.
What has the USA said about this?
"We have $450 billion, $110 billion of which is a military order, but this is equipment and various things ordered from Saudi Arabia", Trump told reporters.
"People fear them. You challenge them, you might end up in prison, and that has happened", he said.
Another official said the president is particularly sensitive about the unpleasant optics of the situation given the proximity of the midterm elections, but it remains unclear whether he will take any action.
Saudi Arabia fired five top officials afterward, including Deputy Chief of General Intelligence Ahmad bin Hassan Assiri, a royal court adviser Abdullah Al-Qahtani, and Mohammed Bin Saleh Al Rumaih an assistant to the intelligence chief.
The incident has grown into a public relations nightmare for the kingdom and the crown prince in particular.
Mr Trump stressed the importance of Saudi Arabia as a counterbalance to Iran in the Middle East, and pushed back against the need for sanctions against the country in light of the new information, talking about the effect of such a move on the U.S. economy.
German Chancellor Angela Merkel said the "horrific events" surrounding Khashoggi's killing "still haven't been cleared up and of course we demand that they be cleared up".
Australia announced it is withdrawing from an investment summit in Saudi Arabia later this month - joining a growing boycott that includes the US, UK, Dutch and French finance ministers over the Khashoggi killing. "This is far from the end and we need to keep up the global pressure".