Turkey has wanted to search the consulate for days.
The search came almost two weeks after Khashoggi, a Saudi critic, vanished after entering the building.
A cleaning crew walked into the consulate hours ahead of the investigative team's arrival.
Local reports based on information provided by unidentified Turkish officials have painted a bleak picture of deceit and murder.
Turkish officials have said they believe Khashoggi - a Washington Post contributor who was critical of Prince Mohammed's policies - was killed inside the mission, and lurid claims have even been leaked that he was tortured and even dismembered.
A trio of crossbench senators is calling for Australia to boycott a major investment forum in Saudi Arabia next week as the kingdom faces a backlash over the presumed death of a journalist at the Saudi consulate in Turkey.
The king phoned Erdogan "to thank the president for welcoming the kingdom's proposal to form a joint working group to discuss the disappearance of Saudi citizen Jamal Khashoggi".
"Saudi Arabia is the biggest economy of the region, and the current reform plans rely on opening it further to private investment", said Karen Young, a political economist who studies the Gulf states.
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The precipitous fall of the market in previous days has alarmed Trump who had tethered his electoral fortunes to soaring stocks. Unusual thing about administration is they crave tax cuts but at the same time they are rising the taxes through tariffs.
Secretary of State Mike Pompeo, hurriedly sent to Riyadh, expected to get more clarity during talks with Saudi leaders Tuesday.
Mr Trump addressed snatched questions from reporters over helicopter engine noise at the White House, describing King Salman's denial as "very, very strong". "It sounded to me like maybe these could have been rogue killers".
"Canada remains very troubled by the disappearance of prominent Saudi journalist Jamal Khashoggi and calls for a through, credible and transparent investigation into the serious allegations about Mr. Kashoggi's disappearance".
The European Union has joined calls for a transparent investigation. Speaking to reporters later in the morning, Mr. Trump suggested Khashoggi may have been murdered by "rogue killers" operating outside the authority of the Saudi government.
"The Kingdom also affirms that if it receives any action, it will respond with greater action", the source added. The Arabic-language daily Okaz wrote a headline yesterday in English warning: "Don't Test Our Patience".
However, the White House brushed aside the Saudi threats, pledging a "swift, open, transparent investigation" into the journalist's disappearance.
Trump made the comment during a "60 Minutes" interview with host Lesley Stahl.
"Saudi Arabia is our ally, not just economically, which the president has correctly referred to, but it's also our No. 1 ally in the region of conflict that matters most to us - which is with the Islamic Republic of Iran", Lieberman said Monday to FOX Business' Maria Bartiromo on "Mornings with Maria".
Aldakhil pointed out that due the economic muscle of Saudi Arabia, which is the destination of ten per cent of the weapons manufactured in the U.S. and is one of the top 20 economies, Riyadh will have as many as 30 different options "without flinching an eye if sanctions are imposed on it".