The Pentagon has said he played a critical role in developing the strategy, which singled out China and Russian Federation as top threats, saying they wanted to "shape a world consistent with their authoritarian model".
Since the resignation, Trump has indicated flexibility on his withdrawal schedule but has also made it clear that he did not intend to keep U.S. troops in "unending wars" for long.
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.
Top advisers to US President Donald Trump met at the Pentagon on Thursday to discuss Syria and other topics, a defense official said.More news: Sandra Bullock Is Not "The Lady From Bird Box", Children
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Shanahan, a former Boeing executive, had been Mattis' deputy and it was unclear how long he will remain acting secretary. 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.
The defence official said Shanahan would later Wednesday attend a cabinet meeting with Trump, the president's first of 2019.
"We have some great allies, but a lot of our allies were taking advantage of our taxpayers and our country", Trump said.
Norquist and Shanahan appear to have a good working relationship, with the comptroller frequently appearing alongside the then-deputy during public appearances in the last few months. Like the Obama administration, Trump's government is concerned by what it calls China's militarization of disputed areas in the South China Sea and by its advances in certain high-tech weaponry.
Shanahan, a native of Washington state, holds a bachelor of science degree in mechanical engineering from the University of Washington and two advanced degrees from the Massachusetts Institute of Technology.