Donald Trump has said Saudi Arabia’s crown prince denies knowledge of what happened to a journalist who went missing after visiting the Saudi consulate in Istanbul, saying answers will be coming “shortly”.

The US president tweeted after a phone call with Crown Prince Mohammed bin Salman about the fate of Saudi writer Jamal Khashoggi, who vanished on October 2 while visiting the consulate to pick up paperwork he needed to get married.

Mr Khashoggi had written columns for the Washington Post that were critical of the crown prince.

Mr Trump said the Saudi heir to the throne “totally denied any knowledge of what took place in their Turkish Consulate”.

He added that the crown prince “told me that he has already started, and will rapidly expand, a full and complete investigation into this matter. Answers will be forthcoming shortly”.

US secretary of state Mike Pompeo travelled to Saudi Arabia to talk to King Salman and the 33-year-old crown prince about the fate of the journalist.

Mike Pompeo with Crown Prince Mohammed bin Salman in Riyadh
Mike Pompeo with Crown Prince Mohammed bin Salman in Riyadh (Leah Millis/Pool via AP)

It comes as a high-level Turkish official said police searching the Saudi consulate found evidence that Mr Khashoggi was killed there.

Authorities also appeared ready to search the nearby residence of the consul general after the diplomat left the country.

Saudi officials have called Turkish allegations that a team of 15 Saudi agents killed Mr Khashoggi “baseless”, but US media reports suggested that the kingdom may acknowledge the writer was killed at the consulate, perhaps as part of a botched interrogation.

The close US ally is ruled entirely by the Al Saud monarchy, and all major decisions in the ultra-conservative kingdom are made by the royal family.

Washington Post publisher and chief executive Fred Ryan said the Saudi government “owes the Khashoggi family and the world a full and honest explanation of everything that happened to him”, noting that Tuesday marked two weeks since the disappearance of the 59-year-old journalist.

“The Saudi government can no longer remain silent, and it is essential that our own government and others push harder for the truth,” Mr Ryan added.

The high-level Turkish official said police found “certain evidence” of Mr Khashoggi’s killing at the consulate.

Police planned a second search at the Saudi consul general’s home, as well as some of the country’s diplomatic vehicles, Turkey’s foreign minister Mevlut Cavusoglu said.

The Saudi Arabia consul's residence in Istanbul
The Saudi Arabia consul’s residence in Istanbul (Emrah Gurel/AP)

Leaked surveillance video shows diplomatic cars travelled to the consul general’s home shortly after Mr Khashoggi went into the consulate.

Consul General Mohammed al-Otaibi left Turkey on Tuesday afternoon, state media reported, just as police began putting up barricades around his official residence.

Saudi Arabia did not immediately acknowledge he had left or offer a reason for his departure.

Earlier in the day, UN human rights chief Michelle Bachelet said the “inviolability or immunity” of people or premises granted under the 1963 Vienna Convention on Consular Relations “should be waived immediately”.

That convention covers diplomatic immunity, as well as the idea that embassies and consulates sit on foreign soil in their host countries.

“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,” Ms Bachelet said.

Turkey had 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.

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

Mr Erdogan told journalists on Tuesday that police sought traces of “toxic” materials and suggested parts of the consulate had been recently painted, without elaborating.