The trailer was immediately pulled on Saturday from AMC Loews Lincoln Square 12 Theatre in Manhattan after complaints from customers.
However, the trailer has now been reinstated, on the proviso it is only shown before PG-13 and Rated-R movies.
Adam Fogelson, president of marketing at Universal, told The New York Times that: "The film is not sanitised or softened, it's an honest and real look at events. If I sanitised the trailer beyond what's there, am I suggesting that the experience will be less real that what the movie itself is?
"We as a company feel comfortable that it is a responsible and fair way to show what's coming."
Under the movie's tagline "On the day we faced fear, we also faced courage", the trailer shows passengers of flight 93 boarding the plane before it took off on its doomed flight for San Francisco.
The trailer intermittently cuts to air traffic controllers as they see the two other hijacked planes crash into the World Trade Centre as the pilot of flight 93 announces terrorists have hijacked the plane.
'United 93' is directed by Paul Greengrass, who is best known for 'The Bourne Supremacy' and is no stranger to controversy having also directed 'Bloody Sunday', which told the story of the 1972 Irish civil rights protest march massacre, and made for TV movie 'The Murder of Stephen Lawrence'.
'United 93' will be premiered at New York's Tribeca Film Festival, which opens on April 25. The Oliver Stone-directed 'World Trade Centre' will also be released in the US this August.
The trailer for 'United 93' is currently being shown in 3,000 cinemas across the US.
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