The eldest son of the murdered Saudi journalist, Jamal Khashoggi, has arrived in the US from Saudi Arabia along with his family.
Salah Khashoggi had previously been barred from leaving Saudi Arabia because of his father's criticism of the country's leadership.
Jamal Khashoggi was murdered in the Saudi consulate in Istanbul three weeks ago, investigators say.
Saudi Arabia's public prosecutor is due to travel to Turkey on Sunday, according to a BBC report.
Saudi officials deny the involvement of the royal family, including de factor ruler Crown Prince Mohammed bin Salman, in the murder.
But Russia has said the royal family should be believed.
"No-one should have any reasons not to believe them," Kremlin spokesman Dmitry Peskov said.
His comments contrast with doubts among Saudi Arabia's Western allies as Riyadh has changed its version of what happened in the consulate on October 2 several times.
Russia is making clear who it is siding with in another sign of the wide geopolitical repercussions stemming from this murder.
What do we know about Salah Khashoggi?
Two days before arriving in the US, Salah Khashoggi was pictured receiving condolences from Crown Prince Mohammed.
He briefly shook hands with the royal and gave what many see as a cold stare during Tuesday's apparently staged meeting.
Some are suggesting the public display may have been the price for being allowed to leave the country.
A US spokesman said Secretary of State Mike Pompeo had told Saudi leaders that he wanted Salah Khashoggi, a dual US-Saudi citizen, to be able to return to the US and was "pleased" that he had been allowed to do so.
Sources close to the Khashoggis told Reuters that he and his family arrived on a flight from Saudi Arabia and joined his mother and three siblings in Washington.
It is not clear how long Salah Khashoggi plans to stay in the US.