"I'm really angry and upset by what was said," Zayn, 21, told the Sun. "I was really ill at the weekend, that's why I couldn't fly to America."
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Zayn Malik has said he is "angry and upset" by Matt Lauer's comments
Matt began the interview with 1D stars Liam Payne, Harry Styles, Louis Tomlinson and Niall Horan by asking, "Let's start with the obvious. Where's Zayn?"
Liam confirmed that the singer had a "tummy bug so he's not very well", adding, "We only found out this morning so we're really sad, he is as well, that he can't be here for our album release."
The presenter continued: "Liam, there's obviously a lot of concern, a lot of fans tweeting overnight, there's been a lot of action on social media about him. Is it something more serious than a minor illness? There have been rumours of substance abuse. What's going on?"
The Today Show host Matt Lauer interviewing One Direction
Shocked Liam replied, "No, he's just got a stomach bug. He's ok. He's just at home. He just needs to rest. He's ok."
A rep for Zayn confirmed that he was taken ill after recording the Band Aid single at the weekend, and was not well enough to fly to the US, adding, "He will join the band for promotion for the new album as soon as he possibly can."
Fans were clearly concerned about Zayn's absence, with the hashtag #GetWellSoonZayn quickly becoming a worldwide trending topic on Twitter.
Zayn and his 1D bandmates have had a busy week; as well as performing alongside the likes of Bono, Ed Sheeran and Ellie Goulding on the new version of Do They Know It's Christmas, they also performed at the Royal Variety Performance where they met the Duke and Duchess of Cambridge.
They released the fourth album, Four, on Monday which looks set to top the charts following the success of its lead single Steal My Girl, which went straight in at number one in the US, and number three in the UK.