Cable network A&E suspended Robertson, 67, from the show this week after he made inflammatory remarks about gay people in an interview with GQ magazine.
Although the gay community has condemned Robertson for his comments, tens of thousands of fans have signed a petition, demanding he be reinstated on the grounds of free speech.
The Robertson family posted a statement on its website Thursday night, saying it does not want to work on "Duck Dynasty" without Phil.
"We want you to know that first and foremost we are a family rooted in our faith in God and our belief that the Bible is His word," the statement said.
"While some of Phil's unfiltered comments to the reporter were coarse, his beliefs are grounded in the teachings of the Bible. Phil is a godly man who follows what the Bible says are the greatest commandments: 'Love the Lord your God with all your heart' and 'Love your neighbor as yourself.' Phil would never incite or encourage hate. We are disappointed that Phil has been placed on hiatus for expressing his faith, which is his constitutionally protected right," the family said. "We have had a successful working relationship with A&E but, as a family, we cannot imagine the show going forward without our patriarch at the helm. We are in discussions with A&E to see what that means for the future of 'Duck Dynasty.' Again, thank you for your continued support of our family."