Police said a fourth person was critically wounded and that the suspected shooter was also dead.
"We ask that our fans keep the UNLV community in their thoughts and prayers," Dayton posted on X.
Alerts went out across the UNLV campus, which is less than two miles east of the Las Vegas Strip, after callers reported an active shooter to police at 11:45 a.m. Wednesday, said Adam Garcia, UNLV's police chief.
Garcia said that campus and local police rushed to the scene, a building housing UNLV's Lee Business School, where two university detectives killed the suspect during a shootout.
Authorities gave the all-clear about 40 minutes after the first report of an active shooter.
Sheriff Kevin McMahill said students had gathered outside the building to eat and play games. If police hadn't killed the attacker, "it could have been countless additional lives taken," he said.
"No student should have to fear pursuing their dreams on a college campus," the sheriff said.
Authorities didn't immediately release any additional details about the shootings, the victims, the suspect or a possible motive.
The Associated Press contributed to this report.