Before the governor made his comments, the N.C.A.A. said that it intended for its men’s and women’s basketball tournaments, which are to involve games in dozens of cities through early April, to proceed as originally planned.

“N.C.A.A. member schools and conferences make their own decisions regarding regular season and conference tournament play,” the association’s president, Mark Emmert, said in a statement. The Centers for Disease Control and Prevention, he noted, had not “advised against holding sporting events.”

“In the event circumstances change, we will make decisions accordingly,” he said.

In a statement later Tuesday, the N.C.A.A. said it was still assessing the effects of the coronavirus on tournaments and would “make decisions in the coming days.”

College sports executives have been studying options for the basketball tournaments as the virus has spread to more states. In interviews in recent days, N.C.A.A. officials described a menu of choices — including consolidating the number of event sites and blocking spectators from attending — but stopped short of making dramatic changes to the tournaments. The officials have also insisted that they would not be guided by fear and would take only so many cues from other organizations that have canceled major events.

“We’re aware that this is happening, and we’re always paying attention to what’s going on and trying to understand the decision-making process that others are using because we’re trying to primarily gather scientific data and also understand what other people in other countries have to bring to bear,” Vivek H. Murthy, a former U.S. surgeon general who is a member of the N.C.A.A.’s top governing body, said in an interview on Saturday.

“But that said,” he continued, “what we’re cautious about is that we don’t want to decisions based on panic, and we don’t want to make them solely based on what organizations are doing.”

Much of the money related to the tournaments stems from television rights deals worth hundreds of millions of dollars each year, but the economic consequences could be wide-ranging if fans cannot buy tickets or do not fill hotels and restaurants in the cities where games are to be played.