Media reports citing Turkish officials have said Khashoggi was killed by Saudi agents within minutes of entering the consulate and that his body was dismembered.
"Turkey should enlist the UN to initiate a timely, credible, and transparent investigation," said Robert Mahoney, deputy executive director of the Committee to Protect Journalists.
"UN involvement is the best guarantee against a Saudi whitewash or attempts by other governments to sweep the issue under the carpet to preserve lucrative business ties with Riyadh." Saudi Arabia has denied any involvement in Khashoggi's disappearance, while President Donald Trump has suggested that "rogue killers" may have carried out the alleged crime.
US Secretary of State Mike Pompeo said in Washington that Saudi Arabia had "a few more days" to wrap up its own investigation and that the United States would decide on a response afterwards.
The Khashoggi affair has triggered a backlash against Saudi Arabia amid reports that Crown Prince Mohammed bin Salman ordered the killing.
Asked about the appeal from the rights groups, a Turkish diplomat told AFP that there was "no need" for a UN investigation for the time being.
"There's no need for the moment to go to the UN," said the diplomat, who asked not to be named.
"The Turkish police and the Turkish prosecutor are doing everything and collecting the evidence to find out what happened and how it happened," he said.
"We don't see it as something that we need because they don't have the expertise. What can the UN do?"
At a news conference held at the United Nations, the rights groups said evidence collected by a UN investigation team could be preserved for use in prosecutions.
The team should have access to all potential witnesses or suspects and recommend avenues for bringing to justice anyone against whom credible evidence is found.
"Partial explanations and one-sided investigations by Saudi Arabia, which is suspected of involvement, aren't good enough, said Louis Charbonneau, UN director at Human Rights Watch.
"Only the UN has the credibility and independence required to expose the masterminds behind Khashoggi's enforced disappearance and to hold them to account." Guterres at the weekend said in a BBC interview that the world should know "the truth" about Khashoggi's disappearance, and expressed fear that such incidents were becoming a "new normal." Amnesty International said Saudi Arabia has the most to gain from an impartial UN investigation.
"Without a credible UN inquiry, there will always be a cloud of suspicion hanging over Saudi Arabia, no matter what its leadership says to explain away how Khashoggi vanished," said Sherine Tadros, head the New York office of Amnesty International.
Reporters Without Borders (RSF) described the suspected murder of Khashoggi as "one of the most shocking and extreme cases in recent years.
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