The consulate itself, where Mr Khashoggi was last seen on 2 October, was searched by Turkish investigators on Monday for the first time.

The consul, Mohammad al-Otaibi has now left Turkey, local media report.

Pressure is growing on Saudi Arabia to give a full explanation of what happened to Mr Khashoggi.

US Secretary of State Mike Pompeo has been meeting Saudi leaders in Riyadh and is expected in Turkey later.

Turkish officials believe Mr Khashoggi was murdered by Saudi agents, but the Saudis have denied this.

Overnight, Turkish police completed a search of the consulate after being allowed in by Saudi authorities.

But, according to Turkish media, Mr al-Otaibi left Turkey on a commercial flight bound for Saudi Arabia hours before his official residence was due to be searched.

The decision to widen the search was announced to reporters by Foreign Minister Mevlut Cavusoglu, who added that he had received no "confession" from the Saudis.

Turkish sources released security video last week of cars with diplomatic plates driving between the consulate and the consul's residence on the day Mr Khashoggi was last seen.

The secretary of state has been meeting King Salman, the powerful Crown Prince Mohammed Bin Salman and Foreign Minister Adel al-Jubeir in Riyadh.

Mr Pompeo thanked the king for his "commitment to a thorough, transparent investigation", state department spokeswoman Heather Nauert said.

The crown prince also agreed on the need for an investigation that "provides answers", she said.

The secretary of state was dispatched to Riyadh on Monday after Mr Trump spoke to King Salman on the phone.

According to Mr Trump, King Salman denied "any knowledge of whatever may have happened 'to our Saudi Arabian citizen'."

The president described the denial as "very, very strong" and raised the possibility that "rogue killers" may have been involved.

A leading Republican senator and defender of US-Saudi links, Lindsey Graham, has been highly critical of the Saudi crown prince.

"This guy's gotta go," he said on Tuesday morning, describing the heir apparent as a "wrecking ball".

By Frank Gardner, BBC News

The recent, highly charged exchange of words between Washington and Riyadh now appears to have given way to a mutual search for the least bad explanation. Both countries' leaders know they have an enormous amount to lose if this affair ends up splitting apart their 73-year-old strategic partnership.

Iran, as the regional rival to Saudi Arabia, would be the prime beneficiary if the Saudis were to lose their defensive US umbrella. President Trump is also correct when he says thousands of US jobs would be lost, with China and Russia to be among those lining up to replace them.

Which begs the wider question: is the West's relationship with Saudi Arabia so important that it outweighs the need to condemn and punish what many believe was a state-sponsored murder of a journalist inside a consulate?

Hence the urgent dispatching of US secretary of state for talks with the Saudi leadership. In private there may well be some strong words, in public both countries may want to present a united stand. But one thing is certain: whatever narrative emerges, the international reputation of the Saudi crown prince and power-behind-the-throne Mohammed Bin Salman will forever be tainted by this affair.

It is still not clear. But unnamed official appears to have told the Associated Press that police found "certain evidence" showing Mr Khashoggi was killed there. No further details were given.

For the first time since the journalist disappeared two weeks ago, Turkish investigators were allowed to enter the building.

Turkish President Recep Tayyip Erdogan gave a further insight into the direction the investigation is taking when he spoke to reporters in parliament.

"My hope is that we can reach conclusions that will give us a reasonable opinion as soon as possible, because the investigation is looking into many things such as toxic materials and those materials being removed by painting them over," he said.

A group of Saudi officials entered first on Monday, followed roughly an hour later by Turkish forensic police.

The Turkish investigators - some wearing overalls, gloves and covered shoes - stayed for about nine hours, leaving in the early hours of Tuesday.

They reportedly took with them samples, including of soil from the consulate garden and a metal gate.

The New York Times and CNN, quoting unnamed sources, reported that Saudi Arabia would acknowledge that Mr Khashoggi's death was the result of an interrogation that went wrong.

The intention had been only to abduct him from Turkey, the sources said.

This may explain in part Mr Trump's "rogue killers" line, though it would still leave questions unanswered.

CNN said the Saudis may argue the operation was conducted without clearance
and those responsible would be held accountable.

The Khashoggi family in Saudi Arabia issued a statement calling for an "independent and impartial international commission".

Mr Khashoggi, a critic of the Saudi government who has written for the Washington Post, was last seen walking into the consulate.

Reports suggest an assault and struggle took place in the consulate after Mr Khashoggi went to get paperwork for his forthcoming marriage.

Turkish sources allege he was killed by a 15-strong team of Saudi agents but Riyadh initially insisted that he had left the consulate unharmed.

Mr Khashoggi was once an adviser to the Saudi royal family but fell out of favour with the country's rulers and went into self-imposed exile. He had obtained US residency.

Speaking to reporters after a phone call with King Salman, he said the Saudi leader had firmly denied knowing what had happened to Mr Khashoggi.

Secretary of State Mike Pompeo is flying to Saudi Arabia immediately.

Turkish police have, for the first time, been inside the Saudi consulate where Mr Khashoggi was last seen.

They entered the building around an hour after a group of Saudi officials.

Speaking to reporters after a phone call with King Salman, he said the Saudi leader had firmly denied knowing what had happened to Mr Khashoggi.

Secretary of State Mike Pompeo is flying to Saudi Arabia immediately.

Turkish police have, for the first time, been inside the Saudi consulate where Mr Khashoggi was last seen.

They entered the building around an hour after a group of Saudi officials.

Turkish officials believe Mr Khashoggi was murdered in the consulate by Saudi agents nearly two weeks ago but Riyadh has always strongly denied this.

However, unconfirmed reports in the US mediasuggest Saudi Arabia is preparing to admit that Mr Khashoggi died as a result of an interrogation that went wrong and that the original intention had been to abduct him.

Meanwhile, Arabic channel Al-Jazeera quotes Turkey's attorney-general's office as saying it has found evidence to back claims that Mr Khashoggi was killed inside the mission.

The issue has strained Saudi Arabia's ties with its closest Western allies.

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," he added. "Who knows?"

The president provided no evidence to back his comment.

A Turkish security source has told the BBC that officials have audio and video evidence proving Mr Khashoggi was murdered inside the building.

On Saturday, Mr Trump threatened Saudi Arabia with "severe punishment" if it emerged that Mr Khashoggi had been killed inside the consulate but ruled out halting big military contracts with Riyadh.

Secretary of State Pompeo's visit to Saudi Arabia will be followed by a stop in Turkey.

Diplomatic pressure is growing on the Saudis to give a fuller explanation.

On Monday, King Salman ordered an investigation into the case.

"The king has ordered the public prosecutor to open an internal investigation into the Khashoggi matter based on the information from the joint team in Istanbul," an official quoted by Reuters news agency said.