WASHINGTON — Secretary of State Mike Pompeo will press Saudi Arabia’s leaders this month on diplomatic conclusions that the kingdom has failed to sufficiently answer for the October killing of the dissident journalist Jamal Khashoggi, a senior American official said on Friday.

Turkish officials have said Mr. Khashoggi, a Washington Post columnist who lived in Virginia, was beaten and dismembered when he visited the Saudi Consulate in Istanbul to get documents for his wedding. After his death, Saudi Arabia removed a few senior officials from their posts, and on Thursday a Saudi court held the first session in the trial of 11 suspects charged with Mr. Khashoggi’s death.

The American official spoke as part of a briefing organized for journalists by the State Department to preview Mr. Pompeo’s visits to eight Arab nations in the Middle East from Jan. 8 to Jan. 15. Four senior officials spoke on the call on the condition of anonymity, which the State Department demands for such briefings.

Separately, the department announced that a senior diplomat, James F. Jeffrey, is the new special envoy coordinating efforts to fight the Islamic State. Mr. Jeffrey will also continue as a special representative on Syria. The previous envoy, Brett McGurk, resigned last month after President Trump announced he was withdrawing all 2,000 American troops from Syria. Defense Secretary Jim Mattis had resigned in protest two days earlier.