MØ then entered around midway through the performance to deliver the chorus.
But the 26-year-old appeared nervous and unsure, and seemed to have trouble keeping up.
After fans criticised the performance on social media, MØ responded via Twitter on Sunday.
She posted a picture of a handwritten note called The Aftermath.
"I was beyond excited," she wrote about the chance to perform on SNL. "But unfortunately I had some technical issues which caused latency on my vocals, and as a result I got confused and my timing was off."
"It pains me and I'm SO sad today," she added. "But life goes on... I'm not perfect never claimed to be, don't want to be, but yeah, sometimes it sucks to be an anti-her.
"Big love to Iggy Azalea and her team who're nothing but supporting and amazing!"
Azalea responded to MØ's letter saying "I know ur amazing, thats why i picked u!", telling the singer to not let the critics knock her confidence.
Meanwhile, Iggy has been slammed for arriving at SNL with a huge entourage.
"Iggy had a ton of people in her entourage," a source told the NY Post's Page Six.
And while the show is used to stars and their large teams, Iggy's group - which included her Black Widow collaborator Rita Ora - was bigger than most.
"[Her entourage] hung out backstage. She had 60 people shoved into her dressing room watching on the TV, crowding into the hall. Rita was asking for alcohol, [but] they don't serve it at SNL."
Watch Iggy Azalea and MØ's SNL performance of Beg For It:
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- Daily Mail