Payne, who shot to global fame with boy band One Direction, died at the age of 31 after falling from a third-floor hotel room balcony in Buenos Aires, triggering an outpouring of tributes from fans around the world.
The statement was signed by singers Harry Styles, Louis Tomlinson, Zayn Malik and Niall Horan.
“In time, and when everyone is able to, there will be more to say. But for now, we will take some time to grieve and process the loss of our brother, who we loved dearly,” Payne’s former bandmates added.
They also said that the memories they shared with him will be treasured forever.
“For now, our thoughts are with his family, his friends, and the fans who loved him alongside us. We will miss him terribly. We love you Liam,” the statement concluded.
Malik also posted on Instagram about the late singer, along with a photo of them dozing off next to each other.
"I lost a brother when you left us and can't explain to you what I'd give just to give you a hug one last time," he wrote.
Auditions for "Britain's Got Talent" in Blackpool, England, were postponed on Thursday "due to the tragic passing of Liam Payne," Applause Store, the ticket provider for the show, said in an Instagram story.