President Donald Trump said Thursday it's a "possibility" that the administration could impose travel restrictions within the U.S. to limit exposure to the coronavirus if certain areas get "too hot."

"We haven't discussed that yet," Trump said when asked about the option at a meeting with Irish Prime Minister Leo Varadkar. "Is it a possibility? Yes. If somebody gets a little bit out of control, if an area gets too hot.

"You see what they're doing in New Rochelle, which is good frankly," Trump continued, referring to the city just north of Manhattan where there is a growing cluster of coronavirus cases. "It's the right thing, but it's not enforced, it's not very strong. But people know they're being watched. New Rochelle, that's a hot spot."

Full coverage of the coronavirus outbreak

Let our news meet your inbox. The news and stories that matters, delivered weekday mornings. This site is protected by recaptcha

Imposing travel limits in the U.S. interior would be a significant step in mitigating cases as coronavirus fears roil the economy and cripple various industries. In a prime-time address to the nation Wednesday night, Trump announced a 30-day travel restriction on travel from many European countries as coronavirus cases rise. There were more than 1,200 cases in 42 states and the District of Columbia as of Thursday, according to the Centers for Disease Control and Prevention. The agency said 36 deaths have been reported.

In New York state, 217 cases of the coronavirus have been confirmed as of Thursday, according to the CDC. Westchester County, where New Rochelle is, had 108 coronavirus cases as of Tuesday afternoon, according to the governor's office. Gov. Andrew Cuomo called New Rochelle "the most significant cluster in the country."

Download the NBC News app for full coverage of the coronavirus outbreak

Washington state has had 366 reported cases and 29 deaths, according to the state's Health Department. California Gov. Gavin Newsom announced Wednesday that mass gatherings of 250 people or more should be postponed or canceled across the state until at least the end of March. Nearly 180 coronavirus cases and a handful of deaths have been reported in California.

Trump defended his restrictions on travel from Europe, which excludes the U.K. and Ireland. He said he did not consult with leaders because he had to "move quickly."

"We get along very well with European leaders, but we had to make a decision, and I didn't want to take time," Trump said. "It takes a long time to make the individual calls, but we are calling, and we have spoken to some them prior to, but we had to move quickly. I mean, when they raise taxes on us they don't consult us, and I think that's probably one and the same."

The president also said he canceled rallies in Nevada and one in Florida and is considering postponing campaign events until the situation starts to improve.

"We need a little separation, until such time as this goes away," he said, adding the "human impact" is more important than the "financial."