Saudi officials have strongly denied any involvement in his disappearance and say that he left the consulate soon after arriving.
Trump told the CBS news show 60 Minutes on Sunday that Saudi Arabia would face "severe punishment" if it is determined Khashoggi was killed inside the Saudi consulate, but Riyadh dismissed the US threat and said it would retaliate if Trump took any action against Saudi Arabia.
"Given there seems to be clear evidence that Mr. Khashoggi entered the consulate and has never been seen since, the onus is on the Saudi authorities to reveal what happened to him", Bachelet said. Turkish officials believe he was murdered by Saudi agents - but thus far the Saudis have denied this.
Saudi Arabia is preparing a report that would admit Saudi journalist Jamal Khashoggi was killed as the result of an interrogation that went wrong, CNN and the Wall Street Journal reported on Monday, citing unnamed sources.
Khashoggi has not been seen since he walked into the Saudi consulate in Istanbul on October 2 to sort out marriage paperwork.
It took 13 days for Saudi authorities to allow Turkish Investigators access to the consulate for investigation.
Surveillance footage leaked in Turkish media shows vehicles moving between the consulate and the consul's home after Khashoggi's disappearance.
"It sounded to me like maybe these could have been rogue killers", Trump said.
The search for what happened to missing Saudi journalist Jamal Khashoggi progressed on several fronts Tuesday, with Turkish crime scene investigators finishing an inspection of the Saudi consulate in Istanbul and U.S. Secretary of State Mike Pompeo going to Saudi Arabia to meet with King Salman.
After his visit to Riyadh, Pompeo will hold talks in Turkey on Wednesday, on the second leg of his trip, the Turkish foreign ministry said.
Khashoggi has written extensively for the Post about Saudi Arabia, criticizing its war in Yemen, its recent diplomatic spat with Canada and its arrest of women's rights activists after the lifting of a driving ban for women.
"We have many overlapping interests, places we work together, places where Saudi Arabia and the United States are trying to achieve important things around the world".
Khashoggi's presence in the Washington area, his insight derived from decades of flitting in and out of the Saudi elite, and his easygoing, scholarly manner made him a go-to source for policymakers and journalists alike.
Pompeo was greeted at the airport by officials including Saudi ambassador to Washington, Prince Khaled bin Salman.
Pompeo addressed reporters Thursday after briefing President Trump at the White House on his talks with leaders in Saudi Arabia and Turkey.
Both men were seen smiling and exchanging pleasantries ahead of a closed-door meeting to discuss the case of Khashoggi, a Saudi citizen and U.S. resident.
Who such killers could be and how it fits into reports of a Saudi team being despatched to the consulate before Mr Khashoggi's arrival will presumably need to covered.
Speaking to the Fox Business Network on Wednesday, Trump again cited counterterrorism cooperation with Saudi Arabia and the kingdom's contracts with USA defense contractors.
Khashoggi told MEE that one of the crown prince's closest aides was the person who first told the journalist he had fallen out of favour with the royal court.
Trump previously warned of "severe punishment" for the kingdom if it was found to be involved in Khashoggi's disappearance, which has spooked investors. Pompeo then met a smiling Prince Mohammed, the heir apparent to the throne of the world's largest oil exporter.
On Monday, however, Trump offered a different theory after speaking by telephone with King Salman.
That could, like Trump's comments, seek to give the kingdom a way out of the global firestorm of criticism over Khashoggi's fate. On Sunday, the oil-rich kingdom suggested retaliation if the US were to impose strict measures.