Payne and Malik rose to global fame as part of the boyband One Direction – created on The X Factor TV show in 2010 – and sang together with bandmates Harry Styles, Louis Tomlinson, and Niall Horan.
Malik left the group in 2015 to embark on a solo singing career, and the band later split in 2016.
The cancellation of Malik’s US shows comes as, Payne’s sister, Ruth Gibbins, earlier on Saturday described her brother as her “best friend” in an emotional Instagram post, external, in which she said the family would “take care” of his son, Bear.
“My brain is struggling to catch up with what’s happening and I don’t understand where you’ve gone,” she said.
“I’d drive to the end of the universe to bring you back.”
Meanwhile in Argentina, Payne’s father, Geoff Payne, on Friday viewed tributes for his son outside the Casa Sur hotel in Buenos Aires.
He was followed by a scrum of photographers as he visited the hotel, prompting fans to shout at the press and attempt to block the building’s entrance to stop them entering.
Geoff Payne also visited the morgue in Buenos Aires to officially identify his son. A federal prosecutor previously told the BBC that his body had been “released”, meaning no further tests were being carried out and identification could take place.