US Secretary of State Mike Pompeo has landed in Riyadh, where he will discuss with Saudi King Salman the disappearance of journalist Jamal Khashoggi.

The State Department retweeted pictures posted by the US mission in Saudi Arabia of Pompeo being greeted by his Saudi counterpart, Adel al-Jubeir, at the airport in Riyadh.

Tensions have risen between Washington and Riyadh over the missing Saudi dissident, who has not been seen since he entered the Saudi consulate in Istanbul two weeks ago. US President Donald Trump promised "severe punishment" if the kingdom's leadership killed him.

Oil-rich Saudi Arabia, which denies any involvement, vowed to respond to steps taken against it with "greater action" and warned of consequences for the global economy.

Following his Riyadh visit, Pompeo is expected to arrive in Turkey on Wednesday to meet Turkish Foreign Minister Mevlut Cavusoglu, state news agency Anadolu reported.

Turkey, where Khashoggi disappeared on October 2, has said it believes he was murdered inside the building, allegations which Saudi Arabia has already denied.

Turkish and Saudi teams wrapped up a nine-hour search of the consulate in the early hours of Tuesday, according to Anadolu. It was the first time Turkish officials had been allowed into the building following Khashoggi's disappearance.

Anadolu shared images of what it said were crime scene investigation units searching the garden and the rooftop of the Saudi consulate. The Turkish team, including prosecutors and police officials from anti-terror and crime scene units, also took on Tuesday soil samples from the consulate garden, Anadolu added.

Police had cordoned off the consulate street in Istanbul's Levent district under heavy security, the report said.