Labour leader Phil Goff said he did not know where Mr McCoskrie was coming from.
"He went to my old school - he should know better," Mr Goff said. "These are folk out there doing their best to stop violence in the home. We know we have got too much of it, let's get in behind them and support them."
White Ribbon Day was started by men in Canada in 1991 after a mass shooting of 14 female students. In New Zealand it is co-ordinated by the Families Commission with a taxpayer-funded budget of $350,000.
The official message on the campaign website is: "Show you're against violence towards women."
That is also the message on posters for a White Ribbon "whanau fun day" to be addressed by Auckland Mayor Len Brown in Manukau Square behind the Westfield shopping centre between 10am and 1pm today.
But posters for a White Ribbon march from Waitakere Hospital to Falls Park in Henderson at 1pm carry a gender-neutral message: "Show you're against family violence in Waitakere."
Mr McCoskrie said the Waitakere message was "fantastic" but he would still not wear a ribbon because the campaign as a whole wanted men to stand up specifically against violence towards women. "It begs the question why isn't it a pledge not to use violence against other men as well, and against children, and against the ex's new partner.
"It's not about 'women's safety last', I'm saying it's about family safety first. I want to expand it to a whole-of-family approach."
A ministry study of all 74 couple-related homicides between 2002 and 2006 found that 70 out of 79 perpetrators were men. The 77 victims included 61 women, 10 new male partners of the women, two men who were killed by women alone and four men killed by men and women acting together.
GENDER ISSUE?
Crime survey
* 5.2 per cent of women and 3.3 per cent of men said they were victims of a "confrontational crime" by their partner such as assault, threat or personal property damage in 2008.
* Homicides70 out of 79 perpetrators of couple-related homicides between 2002 and 2006 were men.
* 61 of the 77 victims were women.
ON THE WEB
whiteribbon.org.nz
familyfirst.org.nz