The refund is in response to an incident in which Dr. David Dao, of Elizabethtown, was violently pulled from his seat and dragged down the plane's aisle.
The City Council is looking for answers about the embarrassing video that has been seen around the world. The head of United's parent company has scrambled to contain the damage to the carrier's reputation.
Attorneys representing a man who was dragged off a United Express flight in Chicago and a member of the man's family are set to talk about the incident on Thursday. Dao refused to leave on his own when he was chosen at random to get off the plane.
United's programs for incentivizing people to volunteer to switch to a later flight, typically in exchange for vouchers that can be redeemed for future travel, work pretty well at the gate, Munoz said.
The Chicago-headquartered airline's share price fell sharply during trading on the morning of 11 April, but largely recovered during the afternoon.
Dao, a 69-year-old Kentucky physician, was captured on video Sunday being hauled off a plane by his arms by security personnel at Chicago's O'Hare Airport. He refused to give up his seat on a flight to Louisville, Kentucky.
Passengers agree to a litany of terms in any airline's "contract of carriage", which they agree to when purchasing a ticket.
The U.S. Department of Transportation announced Tuesday that it is reviewing Sunday's events to see if United violated rules on overselling flights.
Chicago Aviation Commissioner Ginger Evans will also speak.
No eyewitnesses on the plane have suggested that Mr Dao did anything but refuse to leave the plane when he was ordered to do so.
United Airlines CEO Oscar Munoz said he felt "shame" when he saw the viral video of airport police dragging a bloodied passenger from one of his company's flights.
But facing a PR disaster on Tuesday evening, Munoz issued a new statement saying he "continues to be disturbed" by what happened and the airline would "fix what's broken so it never happens again".
Footage has emerged of the moments immediately before the now-infamous forceful removal of a passenger from an overbooked United flight.
Munoz came under fire for praising employees in a memo shortly after the incident and not issuing an apology to Dao for two days.
Now, Munoz said he is shouldering the blame for his employees' apparent lack of "common sense".
The passenger, who has since been identified as Dr. David Dao, has hired lawyers to look into his situation.
Dao was ultimately convicted in late 2004 of several counts of obtaining drugs by fraud or deceit and was placed on five years of supervised probation and surrendered his medical license.