Saudi Arabia's King Salman also spoke with Turkish President Recep Tayyip Erdogan on Sunday about Khashoggi's whereabouts and are considering establishing a "working group" to discuss the case, Turkish and Saudi state-run media reported.
Khashoggi went missing when he visited the Saudi Consulate in Istanbul.
The incident is threatening to spark a geopolitical crisis as the USA and Turkey demand answers from Saudi Arabia, and the kingdom vows to retaliate against any punitive measures imposed over the critic's fate.
Britain, France and Germany insisted Sunday that "light must be shed" on the whereabouts of journalist Jamal Khashoggi as they called for a credible investigation into his disappearance. The Saudi stock market dropped by 7% on Sunday after Trump threatened of "severe punishment" which spooked investors. This comes after UK, German and French foreign ministers issued a joint statement, calling to identify and punish those responsible for the suspected killing of the Saudi government critic.
"Germany, the United Kingdom and France share the grave concern expressed by others including HRVP [Federica] Mogherini and UNSG [Antonio] Guterres, and are treating this incident with the utmost seriousness".
"I think we need to continue to evaluate the facts and we'll make that decision - I talked to Secretary Mnuchin about it last night, we'll be taking a look at it through the rest of the week", Pompeo, alongside President Trump, told reporters in the Oval Office on Saturday.
"With misgivings emerging about Saudi involvement in the journalist's disappearance, SoftBank's stock price is responding negatively", said Takashi Oikawa, an analyst at Ichiyoshi Securities.
Jamal Khashoggi hasn't been seen since entering the Saudi embassy in Istanbul. While Saudi Arabia and Turkey have already said they would cooperate in a joint investigation, this would be a separate inquiry, the official said.
However, he told CBS News on Saturday that the USA was investigating the case which he called "really bad and disgusting" and that "there will be severe punishment". But Mr Khashoggi's disappearance has led several business leaders and media outlets to back out of the upcoming investment conference in Riyadh called the Future Investment Initiative. Saudi authorities last week agreed to let Turkish officials search the consulate after Ankara sought permission to probe the building on Saudi sovereign territory.
Cengiz added that she had seen reports President Trump wanted to invite her to the White House.
Khashoggi's vanishing, and the grisly allegations of his murder by Saudi authorities, are testing close ties between the Trump administration and its key Arab ally.