Burke called her "least favorite" pairing in an upcoming appearance on the podcast Allegedly with Theo Von and Matthew Cole Weiss.
Burke said working with the 90210 star on the show's fourth season, in early 2007, "made me want to slit my wrists," according to an Allegedly sneak peek from TMZ.
On Sunday night, though, Burke apologized for the remarks, which "seemingly makes light of suicide."
"I've always lived by the rule that if you don't have anything nice to say, don't say anything at all," she tweeted. "Recently and regrettably, I broke that rule. In the heat of an interview conversation, I used a phrase that seemingly makes light of suicide and I deeply regret it. I have many friends and family members that struggle with depression and thoughts of suicide. To have said something that seemingly makes a mockery of what they've gone through and what they live with is something that I apologize for. I never meant to hurt anyone or to trivialize the topic. I was out of line and for that I apologize."
I've always lived by the rule that if you don't have anything nice to say, don't say anything at all. (cont) https://t.co/Fe6KBqjfnG— Cheryl Burke (@CherylBurke) April 17, 2016
In addition to her strongest words for Ziering, Burke also told the Allegedly co-hosts: "The fact that his name's not [pronounced] 'EEE-an' and it's 'EYE-an' makes me want to throw up," Burke, 31, said.
Weiss and Von sympathized with her, saying that there was something off about Ziering's appearance on The Celebrity Apprentice last year and that he seemed "very intense" and in the moment.
"That's the true colors that they didn't show on Dancing with the Stars," Burke said, adding, "Think of spending time with that for like 8-10 hours a day, seven days a week, for three months."
In fact, Burke said she was so unhappy that she privately lobbied to end their partnership that season.
"I was like, 'Hey execs' – I was like crying to the executives – 'is there any way to force us, to just like eliminate us?' " she said on Allegedly.
But the executives said they couldn't do that, Burke said, and she and Ziering, 52, weren't eliminated until the semi-finals. (At the time, she called that finish "well-deserved.")
The full Allegedly podcast will be released on Tuesday on iTunes.
Ziering's rep did not immediately respond to PEOPLE's request for comment.