Michael Hohl and his fiancee, Amber Maxwell said they were en route to get married in Costa Rica when a federal marshal escorted them from the plane before take-off in Houston, Texas.
United has denied a marshal or any other authority was used in the incident which occurred on Saturday.
The airline is under public scrutiny after a video last week of a passenger being forcibly removed from a flight caused outrage.
Speaking about the recent incident, United said: “These passengers repeatedly attempted to sit in upgraded seating which they did not purchase and they would not follow crew instructions to return to their assigned seats.
Michael Hohl and Amber Maxwell were removed from a United Airlines flight (stock plane photo used)
United Airlines has been under public scrutiny over another incident last week
"They were asked to leave the plane by our staff and complied."
According to Mr Hohl, he and Ms Maxwell moved to empty seats after they found another passenger asleep and sprawled across their seats.
As they were the last to board the flight, he claimed they picked seats in the economy cabin a few row up.
He said: “We thought not a big deal, it's not like we are trying to jump up into a first-class seat.
"We were simply in an economy row a few rows above our economy seat."
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We thought not a big deal, it's not like we are trying to jump up into a first-class seat.
After finding out that these seats were classified as “economy plus”, he claims they offered to pay for the upgraded seating but were denied and told to move back to their original seats.
A United spokeswoman later said the airline offered the couple a discounted hotel rate for the night, and rebooked them on a Sunday morning flight.
But Mr Hohl, while accepting the re-booked flight, said they will not be flying United again and described the whole situation as "quite strange."
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.
Dr David Dao, a 69-year-old Vietnamese-American doctor, was seen in video being dragged off a United flight a week ago.
After the incident triggered international outrage, United Chief Executive Oscar Munoz apologised to Dao, his family and its customers, saying the carrier would no longer use law enforcement officers to remove passengers from overbooked flights.