But Riyadh insists that the journalist, a known critic of Saudi King Salman, had left the building and that murder claims are "baseless".
UN High Commissioner for Human Rights Michelle Bachelet on Tuesday urged the Governments of Saudi Arabia and Turkey to "reveal everything they know" about the disappearance and a possible extra-judicial killing of the prominent journalist.
Bachelet urged the authorities of both the countries "to ensure that no further obstacles are placed in the way of a prompt, thorough, effective, impartial and transparent investigation".
She welcomed the agreement that has allowed investigators to conduct an examination inside the consulate and possibly also at the residence of the Saudi Arabian Consul-General in Istanbul.
Bachelet said diplomatic immunity of officials must be "waived immediately" to ensure a prompt and transparent probe.
"In view of the seriousness of the situation surrounding the disappearance of Khashoggi, I believe the inviolability or immunity of the relevant premises and officials bestowed by treaties such as the 1963 Vienna Convention on Consular Relations should be waived immediately," Bachelet said.
She said under international law, both a forced disappearance and an extra-judicial killing were "very serious crimes" and immunity should not be used to impede investigations into what happened and who is responsible.
"Two weeks is a very long time for the probable scene of a crime not to have been subjected to a full forensic investigation," Bachelet said.
Protection from national jurisdictions is bestowed on consular premises and officials by treaties such as the 1963 Vienna Convention on Consular Relations.
"There seems to be clear evidence that Khashoggi entered the Consulate and has never been seen since, the onus is on the Saudi authorities to reveal what happened to him from that point onwards," she said.
The High Commissioner noted that Saudi Arabia and Turkey were both party to the 'UN Convention against Torture and Other Cruel, Inhuman or Degrading Treatment or Punishment'.
They are obliged to take all measures to prevent torture, enforced disappearances and other serious human rights violations to investigate allegations of acts constituting these crimes, and to bring to justice those suspected of committing them, she said.
Speaking to journalists in Geneva amid news reports that details of Khashoggi's death may surface soon, indicating that it was an accident, UN human rights office (OHCHR) spokesperson Rupert Colville said potentially serious crimes had been committed and the perpetrators should be held accountable.
"The one thing we really know as a solid fact is that Khashoggi went into the consulate and he was never seen coming out again," Colville said, adding that it seemed "very probable" that some crime had been committed.
"Enforced disappearance or murder, if that has occurred, extra-judicial killing, either way, those are very serious crimes," he added.
"We all need to know what it was, how it happened and who was responsible and where the evidence leads".
US lawmakers have been demanding scrapping of the $110 billion mega defence deal with Riyadh, whereas heads of several companies, CEOs, newspapers have announced not to attend an upcoming finance conference in Saudi Arabia.
President Donald Trump on Monday talked to the Saudi King, during which the latter flatly denied having any knowledge of the missing journalist.
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