In the US, there are currently 60 cases of coronavirus infection, including 45 in people who were either brought back from the central Chinese city of Wuhan – the epicentre of the outbreak – or from the Diamond Princess cruise ship in Japan, where hundreds of people were sickened.

Globally, some 81,000 people have been infected by the virus, with most cases in China. The death toll so far is 2,770, with more than 50 deaths occurring outside mainland China as of Wednesday.

Asked whether he agreed with Messonnier’s comment on Tuesday, Trump said: “I don't think it's inevitable. It probably will, it possibly will. It could be at a very small level or could be on a larger level. Whatever happens we're totally prepared, we have the best people in the world.”

Did the US overreact to the coronavirus outbreak in China?

Messonnier was not present at Wednesday’s White House briefing, even though other top health officials, including Health and Human Services Secretary Alex Azar and Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases were by Trump’s side.

Trump announced on Twitter earlier on Wednesday that he was holding the press conference, soon after he had returned to Washington from a trip to India. He slammed some news outlets for “doing everything possible to make the Caronavirus (sic) look as bad as possible, including panicking markets, if possible”.

Officials including Azar have defended the administration as it comes under increasing scrutiny from Democrats over concerns that it is not adequately prepared to deal with a possible wider outbreak of Covid-19, the illness caused by the new coronavirus.

“Because of this hard work and the President's leadership, the immediate risk to the American public has been and continues to be low. Our containment strategy has been working,” Azar said at the White House briefing, referring to himself as the chairman of the Trump administration’s coronavirus task force.

Trump said travel restrictions currently in place barring entry to foreigners who have recently been on the Chinese mainland would be removed "when we are at a point when we don't need them".

"We are not going to loosen the travel restrictions, that's what saved us," he said. The president did not rule out imposing such measures on other countries that are currently experiencing outbreaks of the virus. "Depending on what happens we may cut certain additional countries like we have had to do with China," he said

Azar, testifying before a House budget hearing on Wednesday, played down media reports that Trump plans to appoint a coronavirus “czar” out of frustration with the response currently led by the HHS secretary. “This [approach] is working extremely well. If it doesn't or there's a need for a change ... that would be for the president to decide,” he said.

Trump spent much of his time in the White House briefing criticising his political opponents including House Speaker Nancy Pelosi and New York senator Chuck Schumer, both Democrats, for questioning his response to the global spread of the coronavirus, particularly denying entry to the US to foreigners who had recently traveled to China.

He also blamed the Democrats for sharp declines in the stock market this week, arguing that recent debates among the party’s presidential candidates spooked investors more than concern about the spread of Covid-19.

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The Dow Jones Industrial Average fell by 0.46 per cent on Wednesday, extending losses of over 6 per cent since the start of the week. Equity markets in Europe and Asia have also been similarly hammered by growing fears about a global pandemic of Covid-19.

Asked about criticism directed at China for not responding to the novel coronavirus outbreak sooner, Trump also defended Beijing, explaining that he heard from President Xi Jinping in a lengthy phone call with the Chinese leader that health authorities there were succeeding in containing the illness.

Trump said President Xi was "working really hard, he wants this problem solved". He highlighted the gradual decrease in the number of new infections on the mainland in recent days, adding that the figures were "somewhat reliable".

"The numbers seem to be levelling off and going down in China, which is very good news, so we'll see what happens," he added.