Dr Anthony Fauci’s apparent confirmation of a damning report about the Trump administration’s response to the coronavirus outbreak prompted tweets by Donald Trump and a new round of speculation about whether the president will move to fire his top public health expert.

Fauci made the comments on CNN on Sunday morning. Trump reacted angrily, attacking the New York Times and retweeting a message that called for Fauci to be fired.

But on Monday morning, sources did not indicate that Fauci, 79 and director of the National Institute of Allergy and Infectious Diseases since 1984, was in danger of losing his job.

Speculation continued regadless, prompting the White House spokesman Hogan Gidley to say in a statement: “This media chatter is ridiculous. President Trump is not firing Dr Fauci.”

Among Trump administration officials handling the pandemic, Fauci has emerged as the public face of competence. A regular presence beside Trump at White House briefings, he has been praised for walking a fine line, offering trustworthy information about the pandemic while not enraging or dramatically undercutting the president.

As a result of both threats and a wave of unwanted communications from admirers, Fauci’s security detail has been expanded. Elsewhere in the Trump administration, such a change in profile for a relatively minor official has often been a precursor to the president deciding to remove him or her from the building.

On Sunday, Fauci confirmed a New York Times report that said Trump administration officials recommended instituting social distancing in February, to hinder the coronavirus from spreading, but were rebuffed until mid-March.

Asked by CNN’s Jake Tapper if lives would have been saved had social distancing been implemented earlier, Fauci said: “I mean, obviously, if we had, right from the very beginning, shut everything down, it may have been a little bit different. But there was a lot of pushback about shutting things down back then.”

Later Trump retweeted a message from an obscure Republican congressional candidate that included the line “#FireFauci”. By Monday, the hashtag was trending.

At his morning briefing in Albany, New York, Andrew Cuomo was asked about the issue. The governor of the worst-hit state, who had just announced a death toll of more than 10,000, applauded Fauci as an “extraordinary” asset in the fight against Covid-19.

“I think Dr Fauci is great,” Cuomo said. “I think Americans trust him.”

Of the possibility that Trump might fire Fauci, Cuomo added: “As crazy as things get in this world, I can’t imagine that would ever happen.”

In his statement, Gidley accused the media of “attempt to rewrite history”.

“It was Democrats and the media who ignored coronavirus choosing to focus on impeachment instead,” he said, “and when they finally did comment on the virus it was to attack President Trump for taking the bold decisive action to save American lives by cutting off travel and from China and from Europe.

“Dr Fauci has been and remains a trusted adviser to President Trump.”

Privately, Trump has expressed frustration with Fauci and many of the president’s supporters increasingly advocate that the doctor be fired. But Fauci himself has suggested his job is relatively safe.

Asked by Science magazine how he was managing not to get fired, he said: “Well, that’s pretty interesting because to [Trump’s] credit, even though we disagree on some things, he listens.

“He goes his own way. He has his own style. But on substantive issues, he does listen to what I say.”

Trump is weighing whether to reopen the US economy soon, potentially from 1 May. He has indicated he will listen to advisers including Fauci, who with the Food and Drug Administration commissioner, Dr Stephen Hahn, spent Sunday telling TV networks a swift reopening could be a bad idea.

Veterans of both the White House and the federal healthcare bureaucracy still worry that the deciding factor over Fauci’s fate will not be his public advice to Trump, but his unusual public profile.

Some think Trump may have been testing the waters when he posted the retweet on Sunday night. Notably, Fauci has been absent from some White House briefings.

Zeke Emanuel, a special adviser on healthcare for the Office of Management and Budget in the Obama administration, told the Guardian on Monday Fauci was an “incorruptible man who follows the data”.

“[He] understands public health,” Emanuel said. “I mean, he’s a unique character, very unique. He never says what he doesn’t know.”

Emanuel added that during the coronavirus crisis, “the public has faith in [Fauci] and his view is critical”.