President Donld Trunp says, those behind the killing in the Saudi consulate in Istanbul three weeks ago should be in big trouble.
Shortly afterwards, Secretary of State Mike Pompeo said the US would “punish those responsible” and had revoked visas of 21 identified suspects.
The Saudi government has blamed the murder on rogue agents.
But President Erdogan of Turkey has said the journalist was the victim of a carefully planned “political murder” by Saudi intelligence officers and other officials.
Speaking to reporters at the White House on Tuesday, Mr Trump said: “They had a very bad original concept, it was carried out poorly and the cover-up was the worst in the history of cover-ups.
“Whoever thought of that idea, I think is in big trouble. And they should be in big trouble.”
The Saudi government has provided conflicting accounts of what happened to Khashoggi, a US resident and Washington Post contributor. After weeks of maintaining he was still alive, senior officials now say the 59-year-old was murdered in a rogue operation after visiting the Saudi consulate in Turkey.
The Hurriyet Daily news website said two suspicious suitcases containing clothes had been found in a Saudi consular car abandoned in a car-park in Istanbul.
European Council President Donald Tusk said EU member states must pursue the full details of the killing and avoid any “trace of hypocrisy”.
In a speech to the European Parliament, Mr Tusk said he expected member states and institutions to avoid any “ambiguous game”.
Mr Trump’s public criticism of Saudi Arabia on Tuesday was his strongest so far, but he has continued to highlight the kingdom’s importance as a US ally.
In a separate interview with the Wall Street Journal, Mr Trump addressed the possible involvement of Saudi royals in the killing and said he did not believe King Salman had prior knowledge of the operation.
When asked about the possible role of Crown Prince Mohammed bin Salman, the president replied: “He’s running things and so if anybody were going to be [informed], it would be him.”
He said he had questioned the crown prince about Khashoggi’s death, and been told he did not know about the operation when it was being planned.
Asked if he believed the royal family’s denial, Mr Trump reportedly gave a long pause before saying: “I really want to believe them.”
Mr Trump also said US intelligence officials were returning from Turkey and Saudi Arabia with information about the case.
CIA director Gina Haspel has been sent to Turkey. Intelligence officials have shared an audio recording from inside the Saudi consulate with her, the Daily Sabah newspaper says. The reported recording is said to reveal gruesome details of the murder.
The US president appears to have changed his mind on the issue. When asked by a reporter in Arizona a few days ago whether he thought Saudi Arabia’s explanation for Khashoggi’s death was credible, he said: “I do.”
Mr Pompeo said the US was looking into the possibility of imposing sanctions on those believed to be involved in Khashoggi’s killing beyond revoking their visas.
Mr Pompeo said the suspects worked in the Saudi intelligence services, the foreign ministry and the royal court. But a state department official said they would not be named due to “visa confidentiality”.
On Tuesday, Turkey’s president told MPs from his ruling party that the killing of Khashoggi was planned days in advance.
Mr Erdogan said Turkey had strong evidence the journalist was killed in a premeditated and “savage” murder at the Saudi consulate in Istanbul on 2 October.
Mr Erdogan’s address coincided with the start of an investment conference in Saudi Arabia that has been overshadowed by the Khashoggi case. Dozens of government and business leaders have pulled out, but Crown Prince Mohammed bin Salman appeared at the event on Tuesday.
Many world leaders have condemned the murder of the prominent Saudi critic and demanded a full investigation.
King Salman chaired a cabinet meeting on Tuesday, after which a statement said Saudi Arabia would hold to account those responsible for the killing.
State media also said the king and the crown prince had held a meeting in Riyadh with members of the Khashoggi family, including Khashoggi’s son, Salah. The Associated Press reported that Salah had been under a travel ban since last year because of his father’s work.
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