Turkish officials said chief prosecutor Irfan Fidan failed to get answers about the location of Khashoggi's body and who ordered his killing during three days of a joint Turkish-Saudi investigation in Istanbul.
The Post also reported that bin Salman, in conversations with the White House, has described Khashoggi as "a unsafe Islamist", claiming he was a member of the Muslim Brotherhood.
While insisting the United States did not condone Khashoggi's killing, the top USA diplomat said the United States had "deep and long-term strategic relationships" with Saudi Arabia and "we intend to make sure that those relationships remain intact".
Saudi Arabia's Crown Prince Mohammed bin Salman held a rare meeting with American evangelical Christians as the conservative kingdom seeks to open up more to the world and fix an image of religious intolerance.
A Thursday report in The Washington Post said Netanyahu told Trump administration officials that bin Salman was a key strategic partner and a linchpin of the alliance against Iranian encroachment in the region.
Israeli officials confirmed the Post's report to the Ynet news site, saying Netanyahu urged officials in Washington not to allow the close relationship with the Saudi crown prince to be undermined by the incident.More news: Kettering man pays tribute after Leicester City helicopter crash
In a statement to the newspaper, Khashoggi's family denied he was a member of the Muslim Brotherhood and said the murdered writer had himself denied this repeatedly in recent years.
Turkish President Recep Tayyip Erdogan has also called on Riyadh to disclose the identity of an alleged local collaborator said to have been involved in disposing of Khashoggi's body.
The Saudis have given a shifting account of what happened to Khashoggi on October 2.
He entered the consulate to sort out documents for his marriage to his Turkish fiancée, Hatice Cengiz.
Turkey, for its part, said Khashoggi was strangled the moment he entered the Saudi consulate in Istanbul, the city's chief prosecutor said on Wednesday, adding that it was a premeditated murder.
President Trump has said he is "not satisfied" with the Saudi account.
"We're going to find the fact pattern", he said.
US State Department spokesman Robert Palladino on Thursday called for Khashoggi's remains to be located and returned to his family for burial as soon as possible.