The first teaser video shows Charlize Theron's Meredith Vickers discussing the titular ship's outer space mission with scientists Elizabeth Shaw (Noomi Rapace) and Charlie Holloway (Logan Marshall-Green).
Vickers tells the pair that if they discover alien lifeforms they must not "engage them, talk to them. You will do nothing but report back to me".
Rapace's Shaw takes centre stage in the second preview as she runs to evade bellowing eruptions from the surface of planet LV-223.
"You can't let it leave. You have to stop it. If you don't stop it, there won't be any home to go back to," she tells Vickers and Idris Elba's captain Janek.
In the third video preview, the Prometheus crew explore a cave and find themselves confronted by a giant monolithic figure in the darkness.
Murals on the cave walls begin to shift shape, prompting Shaw to panic and ask the others to leave the room.
The final minute-long teaser clip is between David and Charlie, taking place on the deck of the interstellar ship.
"You think we wasted our time coming here, don't you?" asks Charlie.
"You question depends on the understanding of what you hope to achieve by coming here," responds Michael Fassbender's android David.
Prometheus opens in UK cinemas on June 1 and June 8 in the US.