It is now known whether Trump will nominate Shanahan as Mattis's successor or will select someone else.
"As acting secretary of defence, I now look forward to working with President Trump to carry out his vision alongside strong leaders including the service secretaries, the Joint Chiefs of Staff, the combatant commanders, and senior personnel in the Office of the Secretary of Defense", he had said.
Trump said during the cabinet meeting that Islamic State militants should be combated by nations in the region, including USA adversary Iran.
Trump has not specified a time frame for choosing a permanent defense secretary or said whether Shanahan could potentially assume that role.
In his stinging resignation letter, Mattis made little attempt to hide his disagreements with Trump.
One reason Mattis resigned was Trump's surprise decision to order the withdrawal of USA forces from Syria.
"While we are focused on ongoing operations, Acting Secretary Shanahan told the team to remember China, China, China", an anonymous defence official was quoted as saying.
US President Donald Trump and First Lady Melania Trump greet members of the US military during an unannounced trip to Al Asad Air Base in Iraq on December 26, 2018. The US official, who spoke on condition of anonymity, did not elaborate on Shanahan's views on China or what other guidance he gave during the meeting.
"In 2019, the National Defense Strategy remains our guide".
The national defence strategy, released by Mattis in January past year, describes China as "a strategic competitor" that "will continue to pursue a military modernisation program that seeks Indo-Pacific regional hegemony in the near term and displacement of the United States to achieve global pre-eminence in the future".
Shanahan had worked in the private sector and had no military or diplomatic experience when Trump appointed him deputy defense secretary in 2017.
Seth Jones at the Center for Strategic and International Studies think-tank in Washington said Shanahan started the job from a somewhat weaker position, since he did not have the mandate that comes with being a Senate-confirmed defense secretary.
Trump has suggested Shanahan could be acting defense secretary for an extended period of time.
The Trump administration has had a rocky relationship with China.
"The National Defence Strategy is [Mattis'] strategy", Shanahan said. "I have the greatest confidence in his abilities to lead a phenomenally talented team while performing the duties as Deputy Secretary of Defense", Shanahan said in a statement issued later on Wednesday.
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