"It was an unfortunate incident," said Spicer. "Clearly, when you watch the video, it is troubling to see how that was handled."
Multiple videos of the incident posted to social media sparked outrage Monday. In them, the man can be seen being dragged down the aisle of the plane by his arms.
United Flight 3411, operated by Republic Airways, was scheduled to depart Chicago's O'Hare International Airport at 5:40 p.m. local time Sunday, bound for Louisville International Airport.
United told ABC News that it had offered passengers on the plane up to $800 to give up their seats for four crew members who needed to board. No one volunteered, so the airline generated a list of four names to be removed from the flight and re-accommodated, per by the airline's contract of carriage. Three of those people complied, and one did not. That's when the police were called to remove the man.
"The doctor needed to work at the hospital the next day," Twitter user Jayse D. Anspach wrote in a series of tweets accompanied by videos of the incident. "So he refused to 'volunteer.'"
Anspach added, "A couple airport security men forcefully pulled the doctor out of his chair and to the floor of the aisle. In so doing, the doctor's face was slammed against an arm rest, causing serious bleeding from his mouth. It looked like he was knocked out, because he went limp and quiet and they dragged him out of the plane like a rag doll."
The passenger removed from the United plane has been identified as David Dao, a 69-year-old physician from Elizabethtown, Kentucky, specializing in pulmonary disease. In a statement, lawyers for the Dao family said he is at a Chicago hospital undergoing treatment for his injuries.
Spicer said that he was "sure" that President Donald Trump had seen the video. "I don't think anyone looks at that video isn't a little disturbed when another human being is treated that way. But again, I think one of the things that people have to understand is that when there's a potential law enforcement matter, for the president to weigh in, pro or con, would prejudice the potential outcome."
Spicer added: "I think, clearly, watching another human being being dragged down an aisle and watching blood come from their face after hitting an armrest or whatever, I don't think there's a circumstance where you can't sit back and say this probably could have been handled a little bit better, when you're talking about another human being."
Following the incident, one of the law enforcement officers involved was placed on paid administrative duty pending an investigation. The Chicago Department of Aviation said the officer's actions were not in accordance with standard operating procedure and are not condoned by the department.
ABC News' Jeffrey Cook contributed to this report.