The US secretary of state met on Tuesday with Saudi Arabia’s King Salman and his son Crown Prince Mohammed bin Salman over the disappearance and alleged killing at the kingdom’s hands of Saudi writer Jamal Khashoggi at its consulate in Istanbul.

Mike Pompeo smiled and shook hands with both men, who warmly greeted him just hours after a Turkish forensics team finished a search inside the Saudi Consulate, looking for evidence of the Washington Post columnist’s alleged killing and dismemberment.

Police plan a second search at the Saudi consul’s home in Istanbul, a Turkish Foreign Ministry official said, where leaked surveillance footage show diplomatic cars travelled to shortly after Mr Khashoggi’s disappearance on October 2.

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A man walks past the Saudi Arabia consul’s residence, in Istanbul (Petros Giannakouris/AP)

Saudi officials previously have called Turkish allegations that the kingdom killed Mr Khashoggi “baseless”, but reports in US media suggested the Saudis may acknowledge the writer was killed at the consulate.

Saudi foreign minister Adel al-Jubeir greeted Mr Pompeo when he landed in Riyadh.

Soon after, Mr Pompeo arrived at a royal palace, where he thanked King Salman “for accepting my visit on behalf of President (Donald) Trump” before the two went into a closed-door meeting.

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Mike Pompeo, left, meets with Saudi Arabia’s King Salman (Leah Mills/AP)

Mr Pompeo then met a smiling Prince Mohammed, the 33-year-old heir apparent to the throne of the world’s largest oil exporter.

Mr Khashoggi fled Saudi Arabia and took up a self-imposed exile in the United States after the prince’s rise.

“We are strong and old allies,” the prince told Mr Pompeo as journalists watched.

“We face our challenges together, the past, the day of, tomorrow.”

Mr Trump, who dispatched Mr Pompeo to speak to the monarch over Mr Khashoggi’s disappearance, said on Monday after talking with King Salman that the slaying could have been carried out by “rogue killers”.

Mr Trump provided no evidence but that statement potentially offers the US-allied kingdom a possible path out of a global diplomatic firestorm.

“The king firmly denied any knowledge of it,” Mr Trump said on Monday.

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The entrance of Saudi Arabia’s Consulate (Petros Giannakouris/AP)

“It sounded to me like maybe these could have been rogue killers.

“I mean, who knows? We’re going to try getting to the bottom of it very soon, but his was a flat denial.”

However, left unsaid was the fact that any decision in the ultraconservative kingdom rests solely with the ruling Al Saud family.

“The effort behind the scenes is focused on avoiding a diplomatic crisis between the two countries and has succeeded in finding a pathway to deescalate tensions,” said Ayham Kamel, the head of the Eurasia Group’s Mideast and North African practice.

“Riyadh will have to provide some explanation of the journalist’s disappearance, but in a manner that distances the leadership from any claim that a decision was made at senior levels to assassinate the prominent journalist.”

CNN reported that the Saudis were going to admit the killing happened but deny the king or crown prince had ordered it, which does not match what analysts and experts know about the kingdom’s inner workings.

The New York Times reported that the Saudi royal court would suggest that an official within the kingdom’s intelligence services, a friend of Prince Mohammed, had carried out the killing.

According to that reported claim, the crown prince had approved an interrogation or rendition of Mr Khashoggi back to Saudi Arabia, but the intelligence official was tragically incompetent as he eagerly sought to prove himself.

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A Turkish forensic police officer shoots video in a room of Saudi Arabia’s Consulate (Emrah Gurel/AP)

Both reports cited anonymous people said to be familiar with the Saudi plans.

Saudi officials have been in and out of the building since Mr Khashoggi’s disappearance without being stopped.

Under the Vienna Convention, diplomatic posts are technically foreign soil that must be protected and respected by host countries.

Turkey has wanted to search the consulate for days.

Permission apparently came after a late Sunday night call between King Salman and Turkish President Recep Tayyip Erdogan.

The Turkish inspection team included a prosecutor, a deputy prosecutor, anti-terror police and forensic experts, the state-run Anadolu news agency reported.

Certain areas of the consulate were to remain off-limits, although officials would be able to inspect surveillance cameras, Turkish media reported.

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Cleaning personnel enter Saudi Arabia’s Consulate on Monday before the arrival of the search team (Petros Giannakouris/AP)

What evidence Turkish officials gathered at the consulate remains unknown, though Mr Erdogan told journalists that police sought traces of “toxic” materials and suggested parts of the consulate had been recently painted, without elaborating.

Mr Khashoggi has written extensively for the Post about Saudi Arabia, criticising 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.

Those policies are all seen as initiatives of Prince Mohammed, the son of King Salman, who is next in line to the throne.

Prince Mohammed has aggressively pitched the kingdom as a destination for foreign investment.

But Mr Khashoggi’s disappearance has led several business leaders and media outlets to back out of the upcoming investment conference in Riyadh.

Mr Trump previously warned of “severe punishment” for the kingdom if it was found to be involved in Mr Khashoggi’s disappearance, which has spooked investors.

Mr Trump’s warning drew an angry response Sunday from Saudi Arabia and its state-linked media, including a suggestion that Riyadh could wield its oil production as a weapon.

The US president has been after King Salman and Opec to boost production for weeks to drive down high crude oil prices, caused in part by the coming re-imposition of oil sanctions on Iran after the US withdrawal from that’s country’s nuclear deal with world powers.