Trump said he had talked "more than once" and "at the highest levels" to partners in Saudi Arabia, which is one of Washington's closest allies and a key market for the USA weapons industry. Erdogan told Turkish reporters in comments published in newspapers.
"We want to see what's going on there", he said.
"We're being very tough".
"We request that you make a determination on the imposition of sanctions pursuant to the Global Magnitsky Human Rights Accountability Act", they added. "And the reports that a Saudi Arabian journalist may have been tragically murdered in Turkey should be deeply concerning to everyone who cherishes a freedom of the press and human rights across the globe".
Cengiz, who told CNN that she does not feel comfortable enough to give an on-camera interview, said in written answers to questions from CNN's Christiane Amanpour that Khashoggi "may have been kidnapped, abducted, or some harm may have come to him".
CCTV via Hurriyet / Associated Press This image from CCTV video obtained by the Turkish newspaper Hurriyet reportedly shows Saudi journalist Jamal Khashoggi entering the Saudi consulate in Istanbul on October 2, 2018.
In government-aligned newspapers and on social media, many Saudis have advanced a narrative that the accusations are part of an insidious campaign to smear their country - pointing fingers at Turkey, Qatar and the Muslim Brotherhood, an Islamist group that Saudi Arabia and some of its Arab allies consider a terrorist organisation.
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After Trump spoke, the White House said national security adviser John Bolton and White House senior adviser Jared Kushner, Trump's son-in-law, had spoken to Saudi Crown Prince Mohammed bin Salman about the matter on Tuesday.
Saudi Arabia remained silent as the images, though not offering definitive proof about Khashoggi's fate, played across television networks in Turkey and around the world.
He added that the U.S. Secretary of State Mike Pompeo and the U.S. Secretary of Defense James Mattis have said that concrete steps will be taken in the coming days. "We think that there is very little hope that Jamal is still alive".
Khashoggi had been living in self-imposed exile in the U.S. for the past year. Investigators are also zooming in on a vehicle seen entering and leaving the building after Khashoggi went inside. "Silence, denials and delays are not acceptable". Intelligence reports, largely sourced from the USA, suggest Bin Salman had been seeking to lure Khashoggi back to Riyadh.
Saudi Arabia has denied any involvement in Khashoggi's disappearance and said he left the consulate shortly after he entered last Tuesday.
Cengiz wrote that she was "confident in the abilities of Turkish government officials".
Turkish experts invited to Saudi Consulate for probe
Erdogan, who said he was personally following the case, added that Turkey had no documents or evidence at hand regarding the case. Khashoggi was once a Saudi newspaper editor and is a familiar face on political talk shows on Arab satellite television networks.
Saudi Arabia has sent its own security team to work with Turkish counterparts and intends to "chase every lead to uncover the truth behind his disappearance", he said.
Khashoggi vanished on October 2 after entering the Saudi consulate in Istanbul to obtain papers for his pending marriage to his Turkish fiance Hatice Cengiz.
Ankara sought permission Sunday for the search after the foreign ministry summoned the Saudi ambassador for a second time, Turkish television reported.
But State Department deputy spokesman Robert Palladino told reporters they had no such tip.
Turkish officials have said that they believe Khashoggi was murdered and dismembered inside the building by members of an elite "assassination squad".
The issue threatened the strong relationship the Trump administration has constructed with Mohammed Bin Salman.
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