President Donald Trump and Vice President Mike Pence on Saturday announced additional travel restrictions involving Iran and increased warnings about travel to Italy and South Korea to combat the coronavirus after the health officials in Washington state announced the first death in the U.S. from the virus.

Pence, who's been placed in charge of the administration's response, said the U.S. was "expanding existing travel restrictions to include any foreign national who has visited Iran within the last 14 days.”The administration is also urging Americans not to travel to areas of Italy and South Korea that have been struck hard by the virus.

Travel from China to the U.S. has already been restricted and Trump said he was also looking at restrictions on entry from America's southern border.

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“We are looking also southern border,” Trump said, despite the low number of coronavirus cases in Mexico so far. Pressed on the issue, he said, "This is not a border this seems to be much of a problem right now. We hope we won't have to do that.”

“We’re thinking about all borders,” he said at another point.

Health and Human Services Secretary Alex Azar said, “We want to lower the amount of travel to and from the most impacted areas.”

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“This is a basic containment strategy,” he added.

Health officials said in a press briefing Saturday that the person who died is a man in his 50s.

Trump said four other Americans are "seriously ill," and there are currently 22 confirmed cases, not including the nearly four dozen people who were brought back from Asia.

"Additional cases in the United States are likely, but healthy individuals should be able to fully recover and we think that will be a statement we can make with great surety now that we've gotten familiar with this problem," he said. "Healthy people, if you're healthy you'll probably go through a process and you'll be fine."

The briefing came after three new confirmed or presumptive cases of the coronavirus illness COVID-19 contracted from an unknown source were reported Friday, including in California and Washington State. Azar said officials are not recommending restricting travel to those states.

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Robert Redfield, the director of the Centers for Disease Control and Prevention, said, "We should anticipate more cases, but the current risk to the American public remains low."

Pence also stressed "that the average American does not need to go out and buy a mask." He said the government has more than 40 million masks on hand and has contracted with Minnesota-based manufacturer 3M for 35 million more masks per month to ensure they're available for health care providers.

"We're going to lean into this effort and put the health and safety of the American people first," Pence said.

Trump said he'd be meeting at the White House on Monday with the heads of pharmaceutical companies about the prospects of a vaccine. "They'll be coming to the White House, and we're talking about a vaccine and developing very quickly, and they've already started working on it," he said.

Officials have cautioned it will likely take at least a year and a half to develop a vaccine.

At a rally in South Carolina on Friday, Trump defended his administration's handling of the virus and accused Democrats of "politicizing" the issue. "This is their new hoax," he said.

His Democratic rivals blasted the comments. Trump insisted he'd been misunderstood and hadn't referred to the virus itself as a hoax.

He said he was "referring to the action that they take to try and pin this on somebody because we've done such a good job. The hoax is on them. I'm not talking about what's happening here. I'm talking what they're doing. That's the hoax. That's just a continuation of the hoax, whether it's the impeachment hoax or ‘Russia, Russia, Russia’ hoax. This is what I'm talking about. Certainly not referring to this. How could anybody refer to this? This is very serious,” he said.

He said there was still no reason for panic.

"We would respectfully ask the media and politicians and everybody else involved not do anything to incite a panic because there's no reason to panic at all. This is something that is being handled professionally,” he said. "This too will end."