(CNN) President Donald Trump on Sunday announced new coronavirus screening procedures for travelers to the United States, a day after his administration unveiled other measures aimed at containing the COVID-19 virus.

"In addition to screening travelers 'prior to boarding' from certain designated high risk countries, or areas within those countries, they will also be screened when they arrive in America," Trump tweeted Sunday morning.

Asked which countries would fall into the "high risk" designation, Trump mentioned, Katie Miller, a spokeswoman for Vice President Mike Pence, clarified later Sunday that "this will be expanded to Italy and South Korea. Additionally we are currently working on exit screening from South Korea, Italy, and other European Nations as needed." Screening was already in place for those traveling into the US who have been in China in the last 14 days.

In a rare Saturday press conference, the Trump administration announced the State Department would raise the travel advisory level for parts of Italy and South Korea where the coronavirus has spread widely. The administration also announced expanded travel bans on Iran, another country that the virus has ravaged as it spreads across the globe.

Trump and top members of his coronavirus task force have sought to calm fears that sent markets tumbling last week.

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