Turner recently told NME that he takes the insults back, saying: "We love Gary Barlow.
"I think I really offended him a few years ago though, which I'm sorry about. I didn't understand it then. Didn't know what was going on, trying to rustle some feathers."
Turner also said that his band's next album, Suck It and See, will contain more humour than their 2009 release Humbug.
Turner explained: "There were times in the lyrics on Humbug when I went into some corners that I didn't need to. But I went there and I think there's still some humour on that album. But it's definitely more prominent on [Suck It and See]. There's a few more gags. Not just in the words but in the guitar solos as well."
Watch the video for Arctic Monkeys' new track 'Brick By Brick', which was unveiled online last month, below: