Turkish officials say they believe Saudi agents killed and dismembered Khashoggi and say Turkey has audio and video recordings of it. Saudi Arabia has called the allegations "baseless" but has offered no evidence the writer left the consulate.
A team of around 10 Turkish police investigators and a prosecutor had already left after a nine-hour search.
He vanished during a visit to the Saudi Consulate in Istanbul nearly two weeks ago.
Spain, a longtime commercial ally of the government of Riyadh, is joining growing global concern over the writer who vanished on a visit to the Saudi consulate in Istanbul on October 2.
The Saudis launched an internal investigation into the disappearance of Khashoggi earlier on Monday.
Saudi arch-rival Iran said on Monday it would adopt a wait-and-see approach to Khashoggi's disappearance.
Mr Khashoggi, a critic of the Saudi government who has written for the Washington Post, was last seen walking into the consulate on 2 October.
By supporting and hosting Arab dissidents and strongly backing Qatar and the Muslim Brotherhood, Turkey is challenging Saudi Arabia and the status quo.
However, it remained unclear what evidence, if any, would remain almost two weeks after Mr Khashoggi's disappearance. As if to drive the point home, a cleaning crew with mops, trash bags and cartons of milk walked in, past journalists waiting outside the consulate on Monday.
Trump dispatched Secretary of State Mike Pompeo to meet King Salman over the case that has strained the Americans' relationship with the Saudis, carefully cultivated by the U.S. president. The decision to dispatch Pompeo signals how much the crisis over the fate of Khashoggi, a Saudi citizen and U.S. resident who wrote critically of the kingdom's leaders, is threatening to damage USSaudi relations.
"The objective of (Sunday's) message broadcasted by the Saudi national media is twofold: one goal is to satisfy the domestic public opinion that Saudi Arabia and its royal family will not be humiliated and the other goal is to send a message to the US", Mitreski, researcher at the University of Sydney, told AFP.
Saudi stocks recently took a hit as investors fretted over the diplomatic fallout from the affair and the specter of political instability in the kingdom. The kingdom has so far publicly denied involvement in his disappearance.
Benchmark Brent crude is trading at around 80 dollars a barrel and Mr Trump has criticised Opec and Saudi Arabia over rising prices.
The alleged incident led to business executives and media companies pulling out of a major investment conference in Saudi Arabia this month.
The moves by the US executives follow similar withdrawals from the event by JP Morgan & Chase Co Chief Executive Jamie Dimon and Ford Motor Co Chairman Bill Ford on Sunday.
News that the chief executive of Uber, Dara Khosrowshahi, would pull out of the conference drew angry responses across the region.
Bahrain's foreign ministry released a statement on Sunday emphasising the country's support for Saudi Arabia in the face of those trying to harm the kingdom.
The search came after Turkish President Recep Tayyip Erdogan and King Salman also had their first telephone talks since the controversy erupted, in what appeared to be a conciliatory conversation according to official readouts. "But we want to find out what happened and he's got instructions to find out what happened".