WASHINGTON -- US President Donald Trump on Monday said that "rogue killers" could be responsible for the disappearance and alleged death of a Saudi journalist Jamal Khashoggi.

Speaking to the media at the White House's South Lawn before departing to Florida, Trump said that he had talked for about 20 minutes with Saudi King Salman bin Abdulaziz Al Saud, who denied having any information about Khashoggi's case.

"The king firmly denied any knowledge of it," Trump said. "It sounded to me like maybe these could have been rogue killers. I mean, who knows? We're going to try getting to the bottom of it very soon, but his was a flat denial."

"It sounded like he, and also the Crown Prince, had no knowledge," he said.

"I've asked Secretary of State Mike Pompeo to immediately get on a plane, to Saudi Arabia, go to other places if necessary, which he probably will. But with regards to this, go to Turkey if necessary," Trump added. "The King told me that Turkey and Saudi Arabia are working hand-in-hand, very closely, on getting to the bottom of what happened. So we'll see what happens."

Earlier on the same day, Trump tweeted that Khashoggi is not a US citizen and "I am immediately sending our Secretary of State to meet with King!"

A separate brief statement issued by State Department spokesperson Heather Nauert also said that "the President has called for a prompt and open investigation into the disappearance of Washington Post journalist Jamal Khashoggi."

Last week, Trump said during an interview that he will impose severe punishment if Saudi Arabia is confirmed to be behind Khashoggi's alleged death.

However, he refused to tell what measures he would take, only saying that he would not choose to impose sanctions on the country for fear of losing its military sales orders with US companies.

Saudi Arabia on Sunday strongly warned against any threats to exert economic sanctions or political pressure on the kingdom, saying it will respond to any action with greater action as the kingdom plays an influential and vital role in the regional and global security and economy.

Speaking on Monday about the potential cost for Saudi Arabia, Trump only told the media that "the world is watching. The world is talking. And this is very important to get to the bottom of it."

When asked about whether the United States will take the arms deal off the table with Saudi Arabia, Trump said "I'm not taking anything off the table. No, we're going to try and find out."

Also on Monday, investigators entered the Saudi consulate in Istanbul. A Saudi delegation reportedly had entered the consulate one hour before the Turkish police arrived and appeared still to be inside as the search was conducted.

A Saudi delegation arrived in Turkey on Friday to discuss the case with Turkish authorities, following a Turkish presidential spokesperson's announcement that a joint Turkish-Saudi investigation team would be formed upon the kingdom's request.

Khashoggi, a journalist and columnist for The Washington Post, has been missing since he entered the Saudi Consulate in Istanbul on Oct 2.

Unconfirmed reports said that Khashoggi was likely killed inside the compound, which were denied by Saudi officials as "baseless."

Turkish President Recep Tayyip Erdogan on late Sunday held a phone talk with the Saudi King to discuss Khashoggi's disappearance, when he urged Saudi Arabia to explain Khashoggi's fate and provide evidence that Khashoggi exited the building after entering.

France, Germany and Britain on Sunday have expressed concerns over the case, calling for "a credible investigation" into the incident.

In a joint statement, the top diplomats of the three European countries stressed that "all the light must be shed on the disappearance of... Khashoggi," and that "there needs to be a credible investigation to establish the truth about what happened, and, if relevant, to identify those responsible ... and ensure that they are held to account."