The chief executive says no one will be fired over the incident.
CEO Oscar Munoz and other executives apologized again on Tuesday before discussing the airline's latest financial results with analysts and reporters.
The airline suffered a public relations disaster after a video emerged a week ago showing security officers dragging a bloodied passenger off an overbooked United Express flight in Chicago.
According to the senator's staff, the proposed Airline Passenger Bill of Rights will include minimum cash compensation for involuntary bumping, limits on the use of police to remove passengers who refuse to voluntarily give up their seats, and restrictions on the ability of airlines to bump passengers in order to accommodate crew members or elite-level travellers.
Mr Munoz and other executives vowed to treat customers with dignity, and said that what happened to Dr Dao will never happen again. Lawyers for Mr Dao reported that their client, a physician from Pennsylvania, sought treatment for unspecified injuries at a local hospital following the incident.
But he added: "There was never a consideration for firing an employee".
"A lot of people have ideas and thoughts about how we can make things better, but in that segment, there's been a lot of support", said Munoz.
He described the incident as a "system failure across various areas".
Dao's lawyers have taken steps that foreshadow a lawsuit against the airline and the city of Chicago, which operates O'Hare Airport, where the incident took place.
In particular, Mr Apfel believes that the incident should prompt airlines to re-examine their policies and procedures around overbooking flights, as has been called for by several politicians in the wake of the incident.
Even in normal times, airlines closely - even daily - scrutinize numbers such as advance sales and occupancy levels on planes.
Whether business to China will be affected remains to be seen, United President Scott Kirby said on the earnings call.
Dao reportedly yelled that he was being discriminated against for being of Asian descent, a searing allegation given that United controls nearly 20 percent of U.S. airline traffic to China and has a partnership with Air China.