US secretary of state Mike Pompeo said he “did not want to discuss facts” after meeting Saudi Arabia’s King Salman and crown prince Mohammed bin Salman for talks over the disappearance and alleged murder of journalist Jamal Khashoggi.

Donald Trump sent Mr Pompeo to both the kingdom and Turkey this week to compile a report on the situation surrounding the missing Saudi government critic, who has not been seen since 2 October.

Turkish officials believe Mr Khashoggi was murdered inside the Saudi consulate in Istanbul before his body was later removed – a version of events Saudi authorities have denied.

Sitting down for a meeting with the crown prince, Mr Pompeo smiled as the pair exchanged pleasantries and joked about jet lag, before he thanked the leader for hosting him at short notice.

“Saudi Arabia, we are really strong and old allies, so we face our challenges together, the past, the day of, tomorrow,” the prince told the secretary of state.

Mr Trump initially appeared to be taking a hard line against Saudi Arabia over the situation, but has since speculated without evidence Mr Khashoggi may have fallen victim to “rogue killers” and that the Saudis should be given the benefit of the doubt.

Mr Pompeo said Riyadh should be given a few more days to complete its own probe into the disappearance of Mr Khashoggi, a US resident who had written numerous articles for the Washington Post criticising the Saudi regime.

“They're going to do an investigation, and when the investigation comes out we'll evaluate it,” Mr Pompeo told reporters travelling with him.

When asked if Saudi authorities had disclosed whether Mr Khashoggi was alive or dead, the secretary of state claimed the matter had not come up during discussions.

“I don’t want to talk about any of the facts, they didn’t want to either, in that they want to have the opportunity to complete this investigation in a thorough way,” he said.

Jamal Khashoggi: Everything we know

Reports stemming from high-level Turkish officials suggest authorities had found “certain evidence”, possibly an audio recording, of Mr Khashoggi’s death at the consulate.

“We have asked for it, if it exists, I'm not sure yet that it exists, probably does, possibly does,” Mr Trump said when asked about potential video or audio evidence of the killing.

Meanwhile, the Washington Post has published the final column written by the missing journalist, in which he warns governments in the Middle East “have been given free rein to continue silencing the media at an increasing rate”.