It comes after Wallace apologised for suggesting allegations against him came from “a handful of middle-class women of a certain age”.
The TV host had said on Sunday there had been “13 complaints” from “over 4,000 contestants” he had worked with in 20 years on the BBC cookery show.
His comments caused a backlash, with a Downing Street spokesperson describing them as “inappropriate and misogynistic”.
In a new video posted on his Instagram story on Monday, he said: “I want to apologise for any offence that I caused with my post yesterday, and any upset I may have caused to a lot of people.
“I wasn’t in a good head space when I posted it. I’ve been under a huge amount of stress, a lot of emotion, I felt very alone, under siege, yesterday, when I posted it.”
He concluded: “It’s obvious to me I need to take some time out while this investigation is under way. I hope you understand and I do hope that you will accept this apology.”
A BBC News investigation heard from 13 people spanning a range of ages, who worked across five different programmes.
Production company Banijay UK said it has launched an investigation, with which Wallace was co-operating, while the BBC has said it will “always listen if people want to make us aware of something directly”.
People who have come forward with allegations against Wallace include former BBC Newsnight presenter Kirsty Wark, who said he told stories and jokes of a “sexualised nature” in front of contestants and crew when she was on Celebrity MasterChef.
Other allegations we have heard include Wallace talking openly about his sex life, taking his top off in front of a female worker saying he wanted to “give her a fashion show”, and telling a junior female colleague he wasn’t wearing any boxer shorts under his jeans.
BBC News has also spoken to a former MasterChef worker who says he showed her topless pictures of himself and asked for massages, and a former worker on Channel 5’s Gregg Wallace’s Big Weekends, who says he was fascinated by the fact she dated women and asked for the logistics of how it worked.
Another female worker on MasterChef in 2019 says Wallace talked about his sex life; a female worker on the BBC Good Food Show in 2010 says Wallace stared at her chest; and a male worker on MasterChef in 2005-06 says Wallace regularly said sexually explicit things on set.
But some workers have spoken of more positive experiences with Wallace.
One former worker on Inside the Factory told the BBC he made a lot of “dad jokes” but it never went beyond that.
A former MasterChef worker said nothing during her time there was concerning. Another said she didn’t feel there was any malice to his comments, although she understood why some people may have felt uncomfortable.
Wallace has also re-posted comments on social media from former contestants who said they had positive memories of working with him.
He has not responded to requests for an interview from BBC News.