Payne, 31, died on Wednesday after falling from a third-floor hotel room balcony in Buenos Aires, shocking fans of the boy band, one of the most popular of all time.
Investigators in Argentina are working to reconstruct Payne's final hours, after saying the singer's death likely occurred after "some kind of episode due to substance abuse."
Payne's room was found destroyed, with broken objects and furniture, along with alcohol and substances thought to be narcotics.
Payne shot to fame as part of One Direction on Britain's X Factor in 2010, alongside Malik and Harry Styles, Louis Tomlinson and Niall Horan.
"Given the heartbreaking loss experienced this week, I've made the decision to postpone the US leg of the STAIRWAY TO THE SKY Tour," Malik wrote on social media.
Given the heartbreaking loss experienced this week, I've made the decision to postpone the US leg of the STAIRWAY TO THE SKY Tour. The dates are being rescheduled for January and I'll post them as soon as it's all set in the next few days. Your tickets will remain valid for the…— zayn (@zaynmalik) October 19, 2024
Malik had announced the rare tour last month, with five dates in the United States and six in the United Kingdom.
The US dates - to San Francisco, Las Vegas, Los Angeles, Washington and New York - will be rescheduled for January, Malik said, from their previous dates in October and November.
"Love you all and thank you for your understanding," Malik said.
The crooner has been reclusive in recent years, after his high-profile departure from boy band One Direction in 2015 while the group was on tour in Asia. The group broke up a year later.
Malik dedicated a post to Payne on Thursday, writing, "When it came to the music Liam, you were the most qualified in every sense."
In One Direction's early years, Payne was an anchor for the band as one of its most-frequent singers.
"I was always happy to know, no matter what happened on stage we could always rely on you to know which way to steer the ship next," Malik said.
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