Travis and writer/producer Alex Garland issued a joint statement to The LA Times quashing rumours that the helmer had been dismissed.
The duo explained that Dredd is an "unorthodox collaboration" and the situation with Travis was "misinterpreted". Garland added that he is not seeking a co-director's credit.
"During all stages of the filmmaking, Dredd has been a collaboration between a number of dedicated creative parties. From the outset we decided on an unorthodox collaboration to make the film," the statement read.
"This situation has been misinterpreted. To set the record straight, Pete was not fired and remains a central part of the collaboration, and Alex is not seeking a co-director credit. We are all extremely proud of the film we have made, and respectfully suggest that it is judged on viewing when it's released next year."
Dredd is a cinematic reboot based on the popular 2000AD character. The film stars Karl Urban in the title role with Lena Headey and Olivia Thirlby among the supporting cast.
Dredd arrives in theatres in September, 2012.