"I have instructed my attorneys to go through the Museums, and start the exact same process that has been done with Colleges and Universities where tremendous progress has been made," Trump said on Truth Social.
The Smithsonian, which was established in 1846 and includes 21 museums and galleries and the National Zoo, did not immediately respond to a request for comment. Most of its museums are in Washington, DC.
When asked if Trump would threaten funding cuts to the Smithsonian based on the findings, a White House official said "President Trump will explore all options and avenues to get the Woke out of the Smithsonian and hold them accountable."
The White House said last week it will lead an internal review of some Smithsonian museums after Trump earlier this year accused it of spreading "anti-American ideology" and raised alarm among civil rights advocates.
"The Smithsonian is OUT OF CONTROL, where everything discussed is how horrible our Country is, how bad Slavery was, and how unaccomplished the downtrodden have been — Nothing about Success, nothing about Brightness, nothing about the Future," Trump said.
The Smithsonian receives most of its budget from US Congress but is independent of the government in decision-making. Civil rights advocates say Trump's administration is undoing decades of social progress and undermining the acknowledgement of critical phases of American history.
Trump has made threats to cut federal funding of top US educational institutions, citing pro-Palestinian protests against U.S. ally Israel's war in Gaza, transgender policies, climate initiatives and diversity, equity and inclusion programs.
Last month, the government settled its probes with Columbia University, which agreed to pay $US221 million ($A342 million), and Brown University, which said it will pay $US50 million ($A77 million).
Both institutions accepted certain government demands. Talks to settle with Harvard University are ongoing.
