Executive Office Committee chair Ms McLaughlin raised the issue at a meeting on Wednesday in the wake of the murder of Ashling Murphy.
Ms McLaughlin stressed the need to involve the Department of Education and the wider education sector in the campaign.
She pointed to the success of a recent campaign from Greater Manchester Mayor Andy Burnham.
Committee members agreed to write to The Executive Office in support of the campaign.
Said the Foyle: “In the wake of the tragic events of last week we have heard much public discourse about the role men and boys have to play in changing attitudes towards women and girls in our society.
“If we are ever going to see the sea change required to stop women and girls feeling uncomfortable and at risk while just going about their lives then we need men to take responsibility and lead from the front.
“The type of misogynistic attitudes and behaviours that are still all too prevalent in our society do not materialise from thin air, they are learned at home, in schools, colleges, workplaces and friendship groups.
“We need to do everything we can to challenge these outdated attitudes and educate people about what is and isn’t acceptable, particularly from a young age.
“I feel an awareness campaign on social media and possibly television around responsible and supportive behaviour could make a difference.
“It might cause men and boys to stop and think about their behaviour and the way they have behaved towards women in the past.
“I am glad the proposal was supported by fellow committee members and I hope this is something The Executive Office will consider introducing as soon as possible.
“We have a duty to do everything within our power to end the hostile environment that many women and girls experience on a daily basis.”