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The virus that can lead to pneumonia is believed to have originated in a market selling wildlife in the central Chinese city of Wuhan late last year. It has infected about 80,000 people and killed more than 2700, the vast majority in China.
But the number of new coronavirus infections inside China has for the first time been overtaken by fresh cases elsewhere, with Italy and Iran emerging as new epicentres of the rapidly spreading illness.
At a White House briefing with his coronavirus task force on Wednesday, Trump said public health officials were preparing to do "whatever we have to" to deal with the outbreak.
He said he would accept whatever amount of emergency spending Congress decided to allocate, and was not immediately considering travel restrictions to and from countries such as South Korea and Italy that are dealing with outbreaks.
"The risk to the American people remains very low," Trump said, flanked by Pence and public health officials.
"We're ready to adapt and we're ready to do whatever we have to as the disease spreads, if it spreads," he said, adding the spread of the virus in the United States was not "inevitable."
"It probably will, it possibly will. It could be at a very small level, or it could be at a larger level. Whatever happens we’re totally prepared," he said.
Earlier, he accused two cable TV news channels of presenting the danger from the coronavirus in as bad a light as possible and upsetting financial markets, even as public health officials warned Americans to prepare for a likely local outbreak.
Trump wrote on Twitter that CNN and MSNBC, both of which frequently criticise him, "are doing everything possible to make (the coronavirus) look as bad as possible, including panicking markets," adding: "USA in great shape!"
Trump, who is stepping up his re-election campaign ahead of November's presidential election, did not specify what he did not like about the coverage.
Officials at the US Centers for Disease Control and Prevention on Tuesday said the virus' global march had raised concern about its spread in the United States, though it remained unclear when that might happen or how severe it would be.
Global stock markets have slumped in recent days due to worries over a prolonged disruption to supply chains and economies from the disease. Trump has been increasingly alarmed by the drop in US stock markets, which he considers a barometer of the health of the American economy and sees as key to his re-election.
During his recent trip to India, the Republican president praised US health officials while downplaying the virus' potential impact on the United States.
House of Representatives Speaker Nancy Pelosi, a Democrat, on Wednesday dismissed Trump's assertion in India that the coronavirus was under control at home.
"I don't think the president knows what he’s talking about, once again," she told reporters.
US Health and Human Services Secretary Alex Azar on Wednesday said the United States has 59 coronavirus cases, including 42 American passengers repatriated from the Diamond Princess cruise ship docked in Japan.
Azar told lawmakers the United States would be unlikely to take measures such as regional quarantines, which China and other countries have been using, if the United States faced a more severe coronavirus outbreak.
"It is very rare that those types of cordon sanitaire efforts around cities are effective. They usually promote more panic and cause people to actually leave and spread. Now, China's a different government and culture than we have here," he told a hearing.
Dr Anthony Fauci, the head of the US National Institute of Allergy and Infections Diseases, said that while the virus was contained in the United States, Americans must get ready for a potential outbreak as transmissions spread outside of China.
"If we have a pandemic, then almost certainly we are going to get impacted," Fauci told CNN.
The CDC has advised Americans to not visit China and South Korea, and on Wednesday stepped up travel warnings for Iran, Italy and Mongolia over risks from the disease.
It is also considering expanding airport screenings to target passengers from countries that have seen recent spikes in cases such as Italy and South Korea, NBC News reported.
Trump is seeking $US2.5 billion ($NZ3.9 billion) from Congress to boost its virus response. Democrats have warned that amount falls far short of what is needed and have also urged the White House to appoint a "czar" who could coordinate a national response.
Senate Democratic Leader Chuck Schumer on Wednesday called for $US8.5 billion to prepare.
A congressional source said the Democratic-controlled House will attempt to advance a coronavirus emergency funding bill before the next recess, scheduled to begin on March 12.
The level of funding being considered, according to sources, could be in the range of what Congress provided for battling some past virus outbreaks, which they said were in the $US4 billion to $US7 billion range.