In an announcement posted on Instagram, Redzepi stated: “An apology is not enough; I take responsibility for my own actions.
“For anybody questioning what this implies for the restaurant, let me say it clearly: the Noma group at this time is the strongest and most inspiring it has ever been,” he added.
“We’ve been open for 23 years, and I’m extremely pleased with our individuals, our creativity, and the path Noma is heading.”
He said the team would continue their work at the Los Angeles location without him.
Redzepi also resigned from the board of MAD, a non-profit organisation that he founded in 2011, which states on its website that it focuses on helping those who are new to the restaurant industry.
A recent report in the New York Times said dozens of former employees had accused the chef of creating an abusive culture in the kitchen and a toxic work environment, which included verbal threats and physical mistreatment at the eatery he founded in 2003.
“To be sincere with you, I feel the repercussions of staying silent are worse than me talking up and standing with my friends towards violence,” said Jason Ignacio White, former Noma employee.
White said he witnessed widespread abuse during the years he worked for the celebrity chef.
Days later Redzepi responded to the allegations on social media, saying: “To those that have suffered below my management, my dangerous judgement, or my anger I’m deeply sorry and I’ve labored to vary.”
He stated he had “shouted and pushed individuals, appearing in methods which are unacceptable” and shared that he had gone to therapy and found better ways to manage his anger.
But protests took place outside the Noma pop-up location in the neighbourhood of Silver Lake, with some wage-rights groups calling for Redzepi’s resignation.
“Who desires to eat in an surroundings of abuse,” Saru Jayaraman, a member of One Fair Wage, told the BBC’s US media partner CBS News. “Who desires to eat meals that comes from the tears and sweat of people who find themselves struggling?”
Several corporate sponsors, including American Express, withdrew from the 16-week dinner series.
Reservations for the pop-up in Los Angeles value $1,500 (£1,120) per individual and bought out in simply minutes.