The office accused the decision of being “built on baseless allegations and accusations” and described it as a “blatant interference” in the kingdom’s affairs.
The vote was held despite Donald Trump expressing his desire to maintain close relations with the kingdom and its crown prince.
Bob Corker, a member of the Republican party, proposed the legislation. It calls for the Saudi government to ensure “appropriate accountability” for all those responsible for Mr Khashoggi’s death.
The resolution also encourages Saudi officials to release imprisoned women’s rights activists and to increase efforts to enact economic and social reforms.
Mr Khashoggi, a US resident, was killed inside the Saudi consulate in Istanbul on 2 October.
Saudi officials have blamed a “rogue” team of operatives for the killing.
The Senate’s resolution goes on to declare that there is no statutory authorisation for US involvement in the Yemen civil war. It also supports the end of air-to-air refuelling of Saudi-led coalition planes deployed against Houthi rebels.
The Saudi statement on Monday read: “The Kingdom has previously asserted that the murder of Saudi citizen Jamal Khashoggi is a deplorable crime that does not reflect the Kingdom’s policy nor its institutions and reaffirms its rejection of any attempts to take the case out of the path of justice in the Kingdom.”
It continues: “The Kingdom hopes that it is not drawn into domestic political debates in the United States of America, to avoid any ramifications on the ties between the two countries that could have significant negative impacts on this important strategic relationship.”
It is unclear if the US House of Representatives will consider voting for the resolution.
The CIA is reported to have concluded with “high confidence” that the crown prince was involved in the order to kill Mr Khashoggi.
Additional reporting by agencies
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