During a Saturday press conference at the White House, Vice President Mike Pence -- who is leading the coronavirus response -- announced a new ban on travel from Iran. This would cover any foreign national who has visited the country within the last 14 days.
He also said Trump has authorized the State Department to raise its travel advisory to Level Four, which is the highest level, for certain areas in Italy and South Korea that have been hit hardest by the virus.
At the press conference Saturday, Trump also hinted at tightening the U.S.-Mexico border.
The U.S. had issued a travel advisory for China -- the epicenter of the virus -- late last month, warning citizens to avoid the country entirely.
The State Department also issued a travel warning update for Italy on Friday and urged Americans to reconsider traveling there. In Italy, 900 people have been sickened so far and 21 have died.
"Reconsider travel to Italy due to a recent outbreak of COVID-19," the advisory read. "There is an ongoing outbreak of COVID-19 caused by a novel (new) coronavirus in Italy. Many cases of COVID-19 have been associated with travel to or from mainland China or close contact with a travel-related case, but sustained community spread has been reported in Italy."
Since the first cases of the disease were reported in December 2019, at least 2,800 people have died and close to 85,000 have been infected worldwide. Most of the cases, however, are in mainland China.
Trump called for calm on Saturday and tried to reassure the nation that the threat was under control.
"There's no reason to panic at all. This is something that is being handled professionally," he said.
There are 22 patients in the United States who have coronavirus, Trump said. One medically high-risk patient passed away overnight, but the remaining patients are at varying levels of recovery and were all allowed to return home.
"Unfortunately, one person passed away overnight," the president said. “She was a wonderful woman, a medically high-risk patient in her late 50s. Four others are very ill. Thankfully 15 are either recovered fully or they're well on their way to recovery. And in all cases, they've been let go in their home."
The virus is thought to have contributed to the volatility experienced by the stock market this week after the Dow plunged more than 3,500 points -- the worst decline since the 2008 global financial crisis.
The president told Americans to brace for more coronavirus cases but claimed healthy individuals are likely to recover. Elderly patients and those with certain underlying medical conditions are at a higher risk and must exercise vigilance and caution.
"Our country is prepared for any circumstance," he had said following a coronavirus task force meeting in the White House situation room.
Fox News' Marisa Schultz and Louis Casiano contributed to this report.