Trump, who has forged closer ties with Saudi Arabia and the 33-year-old Crown Prince Mohammed bin Salman, acknowledged for the first time on Thursday that Khashoggi, a USA resident and Washington Post columnist, had likely been killed.
"Trump's getting some criticism for his bold soft-on-murder stance, but some people still have his back", Colbert said, showing a clip of televangelist Pat Robertson "downplaying Khashoggi's murder and prioritizing the financial benefit of siding with Saudi Arabia", notably when it comes to arms sales.
Mr Pompeo said that he recommended President Trump give the Saudis and Turks "a few more days" to investigate.
Corker, along with like-minded Democrats, has invoked the Global Magnitsky Act to compel Trump to report to Congress on the issue of sanctions over the alleged killing of Khashoggi, which could extend to the Saudi Crown Prince Mohammed bin Salman. The White House has reportedly already been briefed on the matter, according to the Times.
Saudi Arabia has denied the allegations.
But, Trump added, referring to ongoing probes by Saudi Arabia and Turkey: "We're waiting for the results of about three different investigations".
The fate of Khashoggi, a prominent journalist and vocal critic of Saudi Arabia's policies, remains unclear more than two weeks after he entered the Saudi Consulate in Istanbul but never emerged.
Saudi Arabia has denied the claims, and initially insisted Mr Khashoggi had freely left the embassy.
In his remarks, Mr Pompeo stressed the long alliance between the United States and Saudi Arabia.
Trump also said on Tuesday that the criticism against the Saudi Kingdom amid the Khashoggi investigation was another instance of "guilty until proven innocent".
Asked what could have happened to Khashoggi, he said, "There are lots of stories out there about what happened, and I'm going to allow the process to move forward and allow the facts to unfold, and.we will make a determination for ourselves about what happened there, based on the facts that are presented".
Several sources told CNN how Turkish officials responded after Khashoggi's fiancée, Hatice Cengiz, sounded the alarm just before 5 p.m. October 2 - 3½ hours after he entered the consulate.
Stephen Colbert has mocked President Donald Trump for his perceived soft-pedaling of suspicions that Washington Post columnist Jamal Khashoggi was murdered in a Saudi Arabian consulate. The prince is next in line for the throne held by his aged father King Salman.
"They also assured me that they will conduct a complete, thorough investigation of all of the facts surrounding Mr Khashoggi, and that they will do so in a timely fashion, and that this report itself will be transparent for everyone to see, to ask questions about, and to inquire with respect to its thoroughness", he said.