Furthermore, they write that with time, there will be more to say.
"But for now, we will take some time to mourn and process the loss of our brother, whom we loved highly. The memories we shared with him will forever be preserved", they continue.
"We will miss him terribly. We love you Liam."
The statement is signed by Niall Horan, Harry Styles, Louis Tomlinson, and Zayn Malik.
One Direction was formed in the British talent show "X-factor" in 2010. In 2016, the band took a break and has not performed together since then.
On Thursday, Argentine media reports that the autopsy report regarding Liam Payne's death is already complete.
The newspaper Clarín writes that they have seen the autopsy protocol and that the doctors have established that the cause of death was "external and internal bleeding", and that the head injuries were severe enough to have caused his death.
Liam Payne died after falling from the third floor of a hotel in Buenos Aires late on Wednesday evening, Swedish time.
