Keith Brown said he was satisfied the group, led by Baroness Helena Kennedy QC, was making “good progress” and the Scottish Government would “act swiftly” on its advice.
However, he disagreed with Prime Minister Boris Johnson that it was possible to “rule out” the stand-alone offence.
The issue of the policing of crime against women has gained prominence since the murder of Sarah Everard by Wayne Couzens, a serving officer with the Metropolitan Police.
The case has also sparked debate about women's safety, as well as trust in the police and criminal justice system.
Mr Johnson has said he does not support calls to designate misogyny as a hate crime, insisting there is “abundant” existing legislation to tackle violence against women.
But addressing Holyrood on Tuesday, Mr Brown said “he would not agree” with Mr Johnson that “it is possible at this stage to rule out the need for a stand-alone offence of misogyny”.
He said any further legislation should be based on the evidence laid out by Baroness Kennedy’s group and the subsequent consultation.
Mr Brown said the independent working group, which is due to report back in February 2022, was looking at whether there were “gaps in the law” which require to be remedied, and whether to add the characteristic of sex to the Hate Crime and Public Order Scotland Act.
When that legislation was passed by MSPs in March, an amendment from Scottish Labour’s Johann Lamont that would have included women as a protected group under the new law was defeated.
The discussion was brought by a topical question from Beatrice Wishart, the Scottish Liberal Democrat MSP. She warned women have to “risk assess” every minute of every day, and said there was a need for a commission to look into violence against women and girls.
“This problem cannot be answered through existing strategies,” she stressed.
Mr Brown said there was a need for the government to take forward further strategies and for men and boys to assess their attitudes to women.
He pointed out the government worked “very closely” with Police Scotland and the Crown Office to tackle all forms of gender-based violence, and said it was investing over £100 million to support frontline services and focus on the prevention of violence against women and girls.
But he added: “Recent tragic cases and the experiences of far too many women show that more needs to be done.”
Ms Wishart said delays in the justice system exacerbated by the pandemic meant women were “suffering in the aftermath” of violent incidents. She said one of her constituents was due to have her case heard at court some five years after the initial alleged offence occurred.
“Court budgets operate on a shoestring and women disproportionately suffer as a result,” she said.
Mr Brown replied the government was tackling the backlog via a £50m investment and the establishment of remote juries.