Mattis had planned to stay as Pentagon chief through Feb 28 to ensure a smooth transition but Trump announced on Dec 23 that he will have a new secretary by Jan 1.
A day earlier, at a White House meeting with congressional leaders, Trump called Mattis "our great military genius".
The immediate reason for Mattis' resignation was Trump's announcement that he is ordering United States troops out of Syria.
During a rambling monologue to White House journalists at the start of a cabinet meeting, Trump lashed out at his former defense secretary even as his replacement, Patrick Shanahan, sat at the president's side.
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Several candidates long rumoured to be interested in the post had indicated in recent days, some publicly, that they did not want to succeed Mattis, who was respected in the Pentagon and enjoyed bipartisan support when he departed on December 31.
He added, "President Obama fired him, and essentially so did I". "Also - looking at the bigger picture for our countries - if what we mutually seek is a partner, then we will likely get a partner". Mattis and other Trump advisers tried unsuccessfully to persuade Trump to stay in Syria long enough to ensure that the Islamic State group, which has largely been defeated on the battlefield, can not regroup. 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.
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.
Shanahan, a former Boeing Co. executive, is confronted with the Syria pullout, a move that drew bipartisan hysteria.
As acting secretary, Shanahan, 56, has all the authority of a permanent secretary. Before that, he spent more than 30 years at Boeing.