"I'm not happy with what [he has] done in Afghanistan - and I shouldn't be happy", said Trump, as Shanahan sat by his side.
The remarks put Shanahan in a hard position from the start of what could be a long tenure at the Pentagon, where many staff were loyal to Mattis.
"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 Wednesday in a statement. "It is an honour to work with such a dedicated team committed to the greatness of our nation", he had said.
In his stinging resignation letter, Mattis made little attempt to hide his disagreements with Trump.
Shanahan provided his view of long-term competition with China and Russian Federation while speaking at an Armed Forces Communications and Electronics Association event last February.
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His new role will see him dealing with China and the planned withdrawal of United States troops from Syria.
"We have some great allies, but a lot of our allies were taking advantage of our taxpayers and our country", Trump said.
In his Cabinet meeting remarks with reporters present, Trump said he was in no rush to get USA troops out of Syria but did not clarify a timetable.
"It's sand and it's death", he said.
Shanahan must oversee the pace at which the USA pulls some 2,200 troops out of Syria, following the president's decision to exit the war-torn country. Nor did the president clarify plans in Afghanistan, where he has ordered a troop reduction on an unspecified timetable.
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In a letter to investors Wednesday, CEO Tim Cook explained that Apple is grappling with several issues, many related to China. Cook said the company expects revenue of $84 billion in the last quarter of 2018, $7 billion less than analysts had forecast.
At his confirmation hearing to be deputy, the late senator John McCain said a lack of detail in some of Shanahan's foreign policy answers was "almost insulting", and he expressed concerns that putting a former defense executive in the Pentagon could be akin to putting a fox "back in to the henhouse".
In announcing Norquist as the Pentagon's new No. 2, Shanahan said the Department of Defense "chief financial officer and comptroller for the past 19 months. has had insight into virtually every tenet of this department", according to the official.
Other officials have described Shanahan as an advocate of the Pentagon's toughening stance toward Beijing.
The Trump administration has had a troubled relationship with China.
Shanahan had worked in the private sector and had no military or diplomatic experience when Trump appointed him deputy defense secretary in 2017.
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Pour rappel, la garde à vue de Carlos Ghosn a été prolongée le 31 décembre de 11 jours, soit jusqu'au 11 janvier 2019. L'audience qui se tiendra devant un tribunal de Tokyo " va être très importante ", ajoute-t-il.
During Shanahan's tense Senate confirmation hearing in 2017, the committee's then-chairman, John McCain, voiced deep concern about giving the deputy job to an executive from one of the five corporations accounting for the lion's share of U.S. defense spending.