Providing workplace protections for victims of abuse so they can stay in work was critical to reducing the effects of violence, she said.
Set start and finish times can make victims vulnerable to abusers who know when and where they will be leaving work. Also, juggling court dates and counselling with childcare and work was often a struggle for those trying to leave an abusive situation.
"My core message is that this bill can save lives. It can protect women and children from the effects of domestic violence," Logie said.
"These workplace protections will help victims to keep their jobs and provide them with a pathway to safety."
Several businesses, including the Warehouse, ANZ and Countdown, already had domestic violence policies in place.
Countdown spokesman James Walker said the company provided 10 days of domestic violence leave a year in its policy introduced late last year.
"With this bill, it is an opportunity for us all to think about what more we can do to end this sort of unacceptable violence in New Zealand, and the role business can play."
Walker said Countdown would be happy to speak to any business wanting to learn more about its policy and how it worked.
"We would encourage any business in New Zealand to do what they can to support their team who are affected by family violence."
Logie supported Countdown and other businesses voluntarily adding domestic violence leave provisions but said such policies should be legislated rather than industry-led.
"I don't want it to come to luck about whether your employer has heard about this and put these policies in place.
"I want our country to send a really clear message that the lives of victims are really important to us and we're going to play a role in protecting them."
Former National MP and Equal Employment Opportunities Commissioner Dr Jackie Blue was also strongly in favour of the bill.
The Human Rights Commission is campaigning for businesses to introduce family violence policies in the workplace.
Like Logie, Blue urged Parliament to vote to send the bill to select committee so the discussion around the issue could begin.
If the bill does reach the next stage, submissions will be sought from a range of people including businesses which already have domestic violence policies, victims, survivors, and their colleagues.
"I'm very hopeful the Government will support it," Blue said.
"That's all we ask, let's get it to select committee. Women's lives depend on it."
Blue said she believed the government would have concerns about costs to small businesses.
"In actual fact, it's a huge saving to employers.
"They can help do the right thing by that person and have a happier, more settled work force by supporting those victims."
Earlier this month the Guardian reported fears businesses would be out of pocket if domestic violence leave was legislated weren't bearing out among those adopting policies voluntarily.
In part this was because most companies had extremely low numbers of staff needing to take domestic violence leave, just a fraction of a per cent for telecommunications company Telstra and Torquay's Surf Coast council.
Family violence leave would cost only 0.02 per cent of payroll and be offset by benefits such as improved productivity, the article said.
