Riyadh announced on Saturday that the outspoken critic of the Saudi regime had died during a “fist-fight” after he entered the building on 2 October.
However, this version of events has been widely disputed and Turkish officials suspect Khashoggi was tortured and then murdered by a team of hit men, before his body was cut up and disposed of.
The US president, who initially said he believed the Saudi account, now says he wants to get to the bottom of what took place inside the consulate.
“We'd like to find out where it is and what happened ... And I think we're inching our way there,” he said, speaking during a trip to Nevada.
Asked if he was happy with Riyadh’s response to the killing – the dismissal of two senior officials and the arrest of 18 people – Mr Trump said more needed to be done.
“No, I am not satisfied until we find the answer,” he said. “But it was a big first step, it was a good first step. But I want to get to the answer.”
The president added he would be seeking talks with crown prince Mohammed bin Salman, the kingdom’s de facto leader.
Meanwhile, German chancellor Angela Merkel has described the Saudi explanation of Khashoggi’s death as “inadequate”.
Her foreign minister, Heiko Maas, said on Saturday that Berlin would reassess its arms sales to the kingdom while investigations into the killing were ongoing.
“As long as these investigations continue, as long as we don't know what happened there, there's no basis for reaching positive decisions on arms exports to Saudi Arabia,” he told public broadcaster ARD.
Saudi Arabia is one of the largest buyers of German arms.
Asked if German companies should decline attending a business conference in Saudi Arabia next week, Mr Maas said he “certainly wouldn't” be attending any events in Riyadh for the time being.
British International Trade Secretary Liam Fox, US Secretary of State Steve Mnuchin and International Monetary Fund chief Christine Lagarde have all pulled out of the investment conference, as well as the CEO of Uber, Dara Khosrowshahi, The New York Times and the Financial Times, among others.
The European Union said the emerging details of Khashoggi's death were “deeply troubling” and that a “continued thorough, credible and transparent investigation” was needed.
The EU said the continuing investigation should bring “proper clarity on the circumstances of the killing and ensuring full accountability of all those responsible for it.”
Speaking on The Andrew Marr Show, on Sunday, UK Brexit secretary Dominic Raab said the Saudi explanation of the killing was not credible.
Britain says it is considering its “next steps” and those responsible for Khashoggi’s death needed to be held to account.
Foreign secretary Jeremy Hunt has previously warned there would be “consequences” for British-Saudi relations if it transpired the Washington Post reporter had indeed been murdered.
Additional reporting by agencies
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