Martin did not say what would happen if that clause fails.
"In my original speech, I would have opened by acknowledging there was a variety of views in my caucus, which is true," she said.
"I was going to make it very, very clear that I was going to speak for myself."
She said she was going to speak about her personal reasons about why she would have been voting in favour of the bill and about her mother's birth mother, Beverly Williams.
"We never knew Beverly, my mother doesn't really remember Beverly – Beverly left her two-year-old daughter and fiver-year-old son in 1943."
Fighting back tears, Martin said it took well into the 1980s for the family to find out what happened to her.
"But that story will have to wait because as often happens in this place evens have moved on and so this speech must change."
Martin said last week she had written a "very different" speech to the one she was giving today.
Instead, her speech focused on the logistics of New Zealand First's position on the bill.
She said on Tuesday, the majority of NZ First's caucus voted that they wanted a referendum in the bill.
Martin had been negotiating the bill with Justice Minister Andrew Little since December.
At no point since then had anyone within NZ First raised the prospect of an abortion referendum, she said.
But the caucus decided and "the majority prevails".
She informed the Prime Minister of her decision at 12pm on Tuesday, and told Little an hour later.
Earlier in the week, Deputy Prime Minister and NZ First Leader Winston Peters threw a spanner in the words but saying NZ First wanted any abortion law go before the public as a referendum.
