The statement follows weeks of media reports about the murder at the Saudi consulate in Istanbul on 2 October. The outcome of the talks was not immediately clear.
The senior United Nations official also welcomed the steps taken by Turkish and Saudi authorities to investigate and prosecute the alleged perpetrators.
Khashoggi was a Saudi journalist who went into self-imposed exile in the United States a year ago after falling out with the kingdom's powerful Crown Prince Mohammad bin Salman. "As Saudi public prosecutor, you have to ask that question, so you can reveal it", Erdogan told reporters in Ankara on Tuesday, shortly after the head of the Saudi investigation entered the kingdom's consulate.
The case has put into focus the West's close relationship with Saudi Arabia - a major arms buyer and lynchpin of Washington's regional plans to contain Iran - given the widespread scepticism over its initial response.
Turkey also played a purported audio of the killing for CIA Director Gina Haspel last week.
When news of Mr Khashoggi's disappearance first started to circulate, Saudi Arabia said Mr Khashoggi had walked out of the building alive.
Turkey alleges a Saudi hit squad - including a member of Saudi Crown Prince Mohammed bin Salman's entourage - travelled to Istanbul to kill the journalist and then tried to cover it up.
"For an investigation to be carried out free of any appearance of political considerations, the involvement of global experts, with full access to evidence and witnesses, would be highly desirable", Bachelet said on Tuesday.
Jamal Khashoggi was strangled to death as soon as he entered the Saudi consulate in Istanbul, a senior Turkish official has said. He was headed to Istanbul's Atatürk Airport on Wednesday afternoon after a three-day visit.
U.S. Secretary of State Mike Pompeo and Defense Secretary James Mattis on Tuesday called for a cessation of hostilities in Yemen and urged the start of United Nations -led negotiations to end the civil war next month.
The case has brought near unprecedented worldwide scrutiny on Saudi Arabia and its powerful Crown Prince Mohammad bin Salman, whom Khashoggi had criticized.
Turkey is seeking the extradition of 18 suspects in the journalist's slaying who were detained in Saudi Arabia. Singling out Mr. Trump, she urged him to "help reveal the truth and ensure justice be served". He should not pave the way for a cover-up of my fiance's murder. Let us know whoever this person is and we will find them.
"I believe the Saudi regime knows where his body is", she told the audience at the service, sponsored by the Middle East Monitor and Al Sharq Forum.
"We will continue to campaign for truth and accountability for his horrific murder, by those who planned, ordered and executed it", said Kumi Naidoo, secretary general of Amnesty International, which released the video.
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