The Washington Post, which employed Khashoggi as a columnist, reported last week that the slain journalist's family were given million-dollar homes in the kingdom and five-figure monthly payments as compensation for the killing of their father.
In a statement posted on Twitter by Salah Khashoggi, Jamal's son, the family condemned "recent attempts to smear his legacy and draw friction are ill and immoral".
"Acts of generosity and humanity come from the high moral grounds they possess, not admission of guilt or scandal".
Eleven suspects are on trial for last year's murder of Kashoggi, which the Central Intelligence Agency and some Western governments believe was ordered by Saudi Crown Prince Mohammed bin Salman.
This followed a report that the family was considering accepting financial and material compensation for his death.
The Post, quoting Saudi officials speaking anonymously, reported the payments were approved by King Salman.
The news comes just a day after the U.S. State Department barred entry to 16 Saudi nationals over what it described as their role in the killing of the Washington Post columnist.
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Salah Khashoggi said those who carried out his father's killing will be brought to justice and encouraged anyone with information to come forward.
A bipartisan chorus of US lawmakers has called on the White House to harden its stance toward Saudi Arabia after Khashoggi was killed at the Saudi consulate in Istanbul.
Trump had a "productive conversation" with Mohammed bin Salman about Middle East stability last night, according to a White House statement, reports Bloomberg.
Trump has said the US partnership with Saudi Arabia is important for the USA economy and maintaining stability in the region.
The call comes days after activists told The Associated Press that 12 people with ties to women's rights activists, including two U.S. citizens, were detained last week and have been held incommunicado since.