In a tweet, Trump said that "Reports that H.H.S. Secretary @AlexAzar is going to be 'fired' by me" are false.
The President accused the media of being "...desperate to create the perception of chaos and havoc in the minds of the public. They never even called to ask. Alex is doing an excellent job!"
Azar echoed Trump's message in his own tweet thread later Sunday evening attacking the media and praising the President's coronavirus response.
The pushback came after a senior administration official told CNN on Saturday that White House officials were discussing plans to replace Azar following a spate of criticism over the response to coronavirus outbreak.
Any move to replace Azar would be contingent on Trump deciding to move forward, and there is currently little appetite inside the White House for a big shake up amid the coronavirus pandemic. The official stressed that nothing is imminent, but there are discussions underway at the White House about replacing Azar.
Deputy White House press secretary Judd Deere told CNN on Saturday, "The Department of Health and Human Services, under the leadership of Secretary Azar, continues to lead on a number of the President's priorities. Any speculation about personnel is irresponsible and a distraction from our whole-of-government response to COVID-19."
HHS spokeswoman Caitlin Oakley said on Saturday that Azar "is busy responding to a global, public health crisis and doesn't have time for palace intrigue."
Still, the discussions come after Trump appointed Vice President Mike Pence, rather than Azar, as the White House's point man for coronavirus response at a rare presidential news conference.
Trump had privately expressed frustration over Azar's lack of communication on key issues as the head of the White House coronavirus task force. Azar has also been at odds with Centers for Medicare and Medicaid Services Administrator Seema Verma, an ally of Pence's from Indiana who has been involved in the coronavirus task force briefings, the media reported.
Azar, who joined the Trump administration in January 2018, served as general counsel and deputy secretary of the agency under former President George W. Bush. He then joined Eli Lilly, becoming president of Lilly USA in 2012.
( With inputs from ANI )