"I don't think you're smarter than anybody else, but you've convinced a lot of us you are," Reid told the Las Vegas Asian Chamber of Commerce, according to video posted by Time magazine.
At the same event, Reid also quipped, "One problem that I've had today is keeping my Wongs straight."
Both jokes elicited laughter from the crowd. But, after Time published the video, Reid nevertheless apologized and said they were "in extremely poor taste."
"My comments were in extremely poor taste and I apologize," Reid said. "Sometimes I say the wrong thing."
As The Washington Post noted, Reid has a history of making colorful and sometimes controversial remarks. He once reportedly said President Barack Obama had "no Negro dialect - unless he wanted to have one," for example, and has called Sen. Kirsten Gillibrand (D-New York) "the hottest member" of the Senate.