Mr Trump has repeatedly clashed with the Democratic-controlled House over its moves to investigate his actions or those of his administration.
In recent days, House Speaker Nancy Pelosi and Senate Democratic leader Chuck Schumer have urged wide-ranging investigations into Mr Trump’s handling of the coronavirus outbreak, which has killed tens of thousands of Americans.
Democrats have criticised Mr Trump, saying he has failed to develop a comprehensive and effective plan for testing Americans for the coronavirus and tracing contacts of those who are infected by the virus that causes the sometimes fatal Covid-19 respiratory disease.
Dr Fauci, 79, has had a respectful but sometimes complicated relationship with Mr Trump.
The well-regarded doctor has at times corrected or contradicted the president at White House briefings or in press interviews on issues such as the time required to develop a vaccine and the likelihood that the coronavirus will return in the fall.
Mr Trump has occasionally shown exasperation with Dr Fauci but ultimately has followed, largely, the advice that he and Dr. Deborah Birx, the White House’s coronavirus task force coordinator, have provided on responding to the pandemic.