Trump could face an uphill battle finding someone who can be confirmed by the Senate in the wake of Mattis' acrimonious departure. The former Marine Corps general was one of several national security aides who had persuaded Trump that an ongoing military presence there was critical to defeating the Islamic State and other US security interests.
"While we are focused on ongoing operations, Acting Secretary Shanahan told the team to remember: "China, China, China", said the official, who spoke on condition of anonymity.
On Wednesday, Trump proclaimed to Cabinet members and the assembled press that "as you know, President Obama fired [Mattis], and essentially, so did I".
Trump then asked rhetorically "What's he done for me?"
While White House officials have denied reports that Trump also has ordered half of the 14,000 USA troops in Afghanistan to come home, Trump made it clear he has run out of patience for what's become the longest United States war. However, as Mattis' brutal letter made clear he was leaving of his own accord because Trump's worldview is so discordant with his own.
Shanahan sat next to Trump during a cabinet meeting on Wednesday.
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At the meeting, Shanahan indicated that China would be his top priority. His views on alliance relations and other key defense issues are not well known.
At a morning meeting at the Pentagon with the military service secretaries and other top civilian officials, Shanahan said he was focused on the defense strategy developed during Mattis' tenure.
But defense officials say he will represent some continuity from Mattis, since he helped craft the department's National Defense Strategy - which shifts the Pentagon's focus from counter-terrorism to great power competition with China and Russian Federation. It emphasizes the importance of great power competition with Russian Federation and China, after America's many years of fighting insurgent wars in the Middle East. Shanahan had been the deputy secretary since July 2017.
The Trump administration has had a rocky relationship with China.
Separately, Shanahan's spokesman, Lt. Col. Joe Buccino, said that as part of Shanahan's ethics agreement he had stepped aside himself "for the duration of his service" at the Pentagon from "matters in which the Boeing Company is a party".
David Norquist, the Pentagon's comptroller, will perform the duties of the deputy as well as retain his current title.