President Trump on Monday hinted that he might expand travel restrictions as the outbreak of the coronavirus continues to worsen worldwide.

Speaking during a meeting with pharmaceutical company executives and his coronavirus task force, Trump said his administration is mulling over widening restrictions on travel to and from “certain countries where they're having more of a breakout."

The president declined, however, to specify which countries could be added to that list.

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The U.S. is currently cautioning citizens against any nonessential travel to China and Iran and is prohibiting citizens from those countries from entering the country. China, where the virus first appeared around two months ago, has seen the highest numbers of infections – and deaths – while the outbreak has rapidly killed at least 66 people among 1,501 confirmed cases in Iran.

Globally, the death toll by Monday pushed past 3,000, and the number of people infected topped 89,000, with fast-expanding outbreaks in Iran as well as South Korea and Italy.

South Korea, with the worst outbreak outside of China, said it recorded 599 new cases Monday, bringing the total to 4,335. The death toll rose to 26. To cope, the country said hospitals will be reserved for patients with serious symptoms or preexisting conditions, with mild cases now routed to other designated facilities.

Italy’s infections ballooned 50 percent in 24 hours to 1,694. Health officials in northern Italy sought to bring doctors out of retirement and accelerate nursing students' graduations to help an overwhelmed public health system.

The U.S. has warned Americans against nonessential travel to both South Korea and Italy and warned against older individuals and people with chronic medical conditions going to Japan.

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During his meeting, Trump pressed pharmaceutical executives to quickly develop a vaccine, but even the most optimistic predictions don’t see one coming to market for months.

In China, scientists have been testing a combination of HIV drugs against the new coronavirus, as well as an experimental drug named remdesivir that was in development to fight Ebola. In the U.S., the University of Nebraska Medical Center also began testing remdesivir in some Americans who were found to have COVID-19 after being evacuated from a cruise ship in Japan.

It's not clear how quickly such studies will answer whether any of the drugs help.

Fox News' Kelly Chernenkoff and The Associated Press contributed to this report.