The Committee to Protect Journalists, Human Rights Watch, Amnesty International and Reporters Without Borders said such a probe would prevent a "whitewash" of the alleged crime.
Khashoggi, a legal resident of the US who wrote for The Washington Post, disappeared after entering the Saudi consulate in Istanbul on 2 October.
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. On Thursday, Trump said he now believes Khashoggi is dead and warned of "severe" consequences if Saudi royals were found responsible.
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 US 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.
"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.
The rights groups also criticised Riyadh's own internal investigation into Khashoggi's presumed murder and disappearance.
"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".
Follow us on Twitter: @The_NewArab
