Police Minister Poto Williams says her daughter feels unsafe after hearing the National Party leader say "a lot of people want to bottle" her mother.
Collins, a former police minister, says her comments have been misinterpreted and that she meant "bottle" like a "genie in a bottle".
The statement was reported in an article by Herald senior reporter David Fisher on July 23, covering Collins' visit to the Kerikeri Bowling Club.
"Police Minister Poto Williams: 'Isn't she great?'," Fisher quoted Collins as saying.
"She didn't really mean Williams was great. Rather, she says, 'I think a lot of people want to bottle her'. There's a pause just long enough for the implication to set in, then Collins explains - of course - she means to keep Williams in a bottle like a genie'."
Williams said today there were two interpretations to what Collins had said, one being the "actual use of a bottle to harm someone", which was how Williams said she initially interpreted it.
"I was pretty taken aback, shocked, and my family were pretty distressed. I am pleased [Collins] cleared it up but that does not diminish the distress my daughter and my family are feeling at the moment.
"We are public people, with public lives, but on this occasion my daughter feels unsafe for me and that is not on."
Williams has come under strong criticism from National in recent weeks, with Collins calling for her to be sacked over comments she made to Newstalk ZB defending her view that not all police officers should be armed because Māori and Pacific communities did not want it.
She cited statistics showing Māori and Pacific populations were stopped disproportionately more, charged more, arrested more and on the end of police violence more than other ethnicities.
Collins also has stated she does not believe all police should be armed.
Collins also repeated today that when she said "bottled" she meant "as a genie in a bottle".
"Someone spun it the wrong way, it is incorrect and disgraceful."
She said she meant: "Someone who pops out every now and then and says something stupid. She is the worst police minister I have ever seen."
When asked how she felt about Williams' daughter feeling distressed, Collins said she "didn't see her at the National Party meeting".