The EU's top diplomat Federica Mogherini has called for a thorough investigation into the "deeply troubling" death of Saudi critic Jamal Khashoggi and full accountability for those responsible.

In a statement, Ms Mogherini said: "The European Union, like its partners, insists on the need for continued thorough, credible and transparent investigation, shedding proper clarity on the circumstances of the killing and ensuring full accountability of all those responsible for it".

German Chancellor Angela Merkel said those behind Mr Khashoggi's death must be brought to book and called for "transparency" from Riyadh.

"Those responsible must answer for their actions," Ms Merkel and German Foreign Minister Heiko Maas said in a joint statement.

"We expect transparency from Saudi Arabia on the circumstances of his death," it said. "Available reports on what happened in the Istanbul consulate are insufficient."

France has also demanded an "exhaustive and diligent investigation" into the death.

"Many questions remain... unanswered. They require an exhaustive and diligent investigation to establish exactly who was responsible and ensure that those guilty of the murder of Mr Jamal Khashoggi answer for their actions," French Foreign Minister Jean-Yves Le Drian said.

"These expectations are all the stronger as our two countries are linked by a strategic partnership that involves frankness... and transparency," he added.

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It comes as Turkey pledged to reveal all details of the death of journalist Jamal Khashoggi after Saudi Arabia admitted he was killed at its Istanbul consulate, state media reported.

"Turkey will reveal whatever had happened. Nobody should ever doubt about it," said Omer Celik, spokesman for the ruling Justice and Development Party (AKP), the Anadolu news agency reported.

Mr Khashoggi, a Washington Post contributor and critic of the Islamic petro-state's powerful crown prince, was last seen on 2 October entering his country's consulate in Istanbul.

Riyadh's admission came after persistent claims by the Saudi authorities that the journalist had left the consulate alive.

The kingdom also announced the sacking of a top intelligence official Ahmad al-Assiri and royal court media adviser Saud al-Qahtani, both top aides to Crown Prince Mohammed bin Salman, who has faced mounting pressure over the Khashoggi affair.

Turkish police and prosecutors this week searched both the consulate as well as the consul's residence in Istanbul.

Mr Celik said it was Turkey's "debt of honour" to reveal what happened.

"We are not accusing anyone in advance but we don't accept anything to remain covered (up)," he said.

Turkish investigators are likely to find out what happened to Mr Khashoggi "before long", a senior Turkish official said.

"We'll find out what happened to the body before long," the official said. "The DNA is being procured from within Turkey. It seems there will be no need to ask Saudi Arabia at the moment."

Mr Khashoggi's killers may have dumped his remains in Belgrad Forest adjacent to Istanbul, and at a rural location near the city of Yalova, a 90km drive south of Istanbul, officials told Reuters on Thursday.

Investigators were still focused on the Yalova and Belgrad Forest areas, and were looking at CCTV footage from near Belgrad Forest, the senior official said.

Turkish President Recep Tayyip Erdogan last night spoke with Saudi King Salman and the two agreed to continue cooperation in the probe.

In public, Mr Erdogan and top government figures have remained extremely cautious, often referring to a prosecutors' investigation and stopping short of pinning the blame on Saudi Arabia.

Staff members of the Saudi Arabian consulate in Istanbul testified to prosecutors yesterday as part of the investigation.

Last night, the Saudi Press Agency, citing the public prosecutor, said: "The discussions between Jamal Khashoggi and those he met at the kingdom's consulate in Istanbul... devolved into a fistfight, leading to his death". 

The kingdom announced that 18 people had been arrested in the ongoing investigation.

The Saudi king also ordered the setting up of ministerial committee under the chairmanship of the crown prince to restructure the kingdom's intelligence agency and "define its powers accurately", state media said.   

The United States warned yesterday of a "wide range" of responses should it determine that Saudi Arabia is behind the death of Mr Khashoggi, as Turkey widened its investigation into the scandal.

President Donald Trump said the United States, which is Saudi Arabia's biggest backer, could impose sanctions over the murder of Mr Khashoggi.

US Secretary of State Mike Pompeo told Voice of America Radio: "We'll certainly consider a wide range of potential responses."

The Trump administration has been notably slow to criticise Saudi Arabia and the situation has presented Mr Trump with one of the most acute foreign policy crises of his nearly two-year-old presidency.

Pro-government Turkish media have repeatedly claimed that Mr Khashoggi was tortured and killed by a Saudi hit squad inside the diplomatic mission, although Turkey has yet to divulge details about the investigation.

The controversy has put the kingdom - for decades a key Western ally and bulwark against Iran in the Middle East - under unprecedented pressure to offer an explanation to take the heat off its rulers.