U.S. President Donald J. Trump delivers remarks at a Keep America Great Rally in North Charleston, South Carolina, United States on February 28, 2020.

President Donald Trump on Monday brushed off concerns that holding rallies presents a public health risk, even as companies are canceling major events and restricting travel.

"These were set up a long time ago," Trump told reporters Monday during his White House meeting with Colombian President Ivan Duque.

"And you could ask that to the Democrats, because they're having a lot of rallies, they're all having rallies, they're campaigning," he added. "I think it's safe, I think it's very safe."

Democratic candidates have yet to cancel their major rallies and events as the field of candidates continues to shrink. Sen. Bernie Sanders, I-Vt., held a rally Sunday in a region of northern California that has reported a few infections of the virus.

Trump, meantime, held a rally Friday night in North Charleston, South Carolina, a day ahead of the state's Democratic primaries. He is scheduled to hold one Monday night in Charlotte, North Carolina, the night before that state's Super Tuesday primary. The GOP will hold its nominating convention in late August in Charlotte.

The Trump campaign did not immediately respond to a request for comment.

Health experts in most states have advised Americans to continue with their normal activity, but use good hygiene, such as washing their hands.

But as confirmed cases continue to rack up, some experts have wondered how much longer campaigns can carry on as normal, without looking irresponsible. As of Monday morning, there were 91 confirmed cases in the U.S. Two people, both in Washington state, have died from the virus. States including California, Illinois and New York now have confirmed cases.

CNN on Monday reportedly said in an internal memo that parent company WarnerMedia's major TV events, such as Democratic debates and NBA/NCAA coverage, will be staffed but limited to "absolutely critical" personnel. CNN is co-hosting the next debate on March 15 in Phoenix, Arizona. A spokesperson for WarnerMedia did not immediately respond to a request for comment.

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A spokesperson for the Democratic National Committee said in a statement to CNBC on Monday that its "number one concern is to ensure all eligible voters are able to make their voices heard without jeopardizing anyone's health and safety." The Democratic National Convention, where the party will pick its presidential nominee, is scheduled to be held in July in Milwaukee.

The spokesperson added that it will "continue to closely monitor as the situation develops."

The campaign for former New York Mayor Mike Bloomberg, who has staked his candidacy in large part to his experience in crisis management, has yet to cancel any events. "We have not pulled down any events but are closely monitoring the situation in multiple cities," a representative said.

The campaign did, however, issue guidelines to its employees for preventing infection and contending with the outbreak. "Events scheduled to take place in an affected city or community would be postponed," according to the memo.

Representatives for candidates Sanders, Sens. Elizabeth Warren, D-Mass., and former Vice President Joe Biden did not immediately respond to requests for comment.