“We are supporting each other the best we can as a family and ask for privacy and space at this awful time,” they said.
Liam was one of five members of One Direction.
The band’s statement added: “We will take some time to grieve and process the loss of our brother, who we loved dearly.” and concluded: “We will miss him terribly. We love you, Liam.”
Harry Styles, former One Direction band member shared a photo of Liam on Instagram, saying that he “lived wide open, with his heart on his sleeve”.
“The years we spent together will forever remain among the most cherished of my life.
“I will miss him always, my lovely friend”.
Fellow member Louis Tomlinson also shared a separate tribute on his personal Instagram account, thanking Payne for being “the kind brother I’d longed all my life for.”
“Reminiscing about all the thousands of amazing memories we had together is a luxury I thought I’d have with you for life,” he wrote.
He added he would also support Liam’s son.
“I want you to know that if Bear ever needs me I will be the Uncle he needs in his life and tell him stories of how amazing his dad was.”
Zayn Malik, who left the band in 2015, also shared a tribute on Instagram alongside a younger photo of him and Payne asleep in a car: “I lost a brother when you left us and can’t explain to you what I’d give to just give you a hug one last time”.
Payne, who found fame on The X Factor in 2010, died after falling from the third floor of a hotel in Palermo, Buenos Aires, police say.
Police inspected the area where he fell, and found items including alcohol and a phone.
Medication was also found in his room.
In a statement, police said Payne’s body was discovered when an emergency crew were called to the hotel and that “everything indicates that the musician was alone when the fall happened”.
They added they believed Payne died at the scene and there were no injuries that suggested a third party had been involved.
Following his death at around 17:00 (21:00 BST) on Wednesday, stars expressed their upset and posted memories of the dad who shared a son, Bear, with former partner Girls Aloud star Cheryl.
Former bandmate Harry’s mother Anne Twist paid tribute, posting a broken-hearted emoji on Instagram, captioning it: “Just a boy.”
Singer Rita Ora, who collaborated on a song with Payne in 2018, said she was “devastated” in a post on Instagram, adding that she “loved working with him so much”.
On Thursday, police in Buenos Aires said a preliminary autopsy suggested the One Direction star died from external and internal bleeding injuries.
They said the area where Payne fell had been inspected and items including alcohol and a phone had been discovered. Medication was found in his room.
Olly Murs, who starred on The X Factor a year before One Direction, also shared his condolences on Instagram, saying he was “lost for words” and described Payne’s death as “devastating”.
Murs said they “always had a good laugh” when they met, mostly talking about “how annoyingly good his hair always looked, or our love for Becks, the old XF [X Factor] days and the tour we shared together.
“Liam shared the same passions as me, the same dreams, so to see his life now end so young hits hard. I’m truly gutted and devastated for his family and of course his son Bear losing a dad.”
Dermot O’Leary, who hosted The X Factor when Liam appeared, posted a photograph of the pair on stage, captioning the Instagram post: “The worst news.”
“I remember him as a 14-year-old turning up to audition on The X Factor, and blowing us away singing Sinatra. He just loved to sing,” he wrote.
“He was always a joy, had time for everyone, polite, grateful, and was always humble.”