The changes in stance for the opposition parties were revealed in the minority reports on the bill in the report back by the select committee.
The issue had been problematic for National's caucus - the more liberal MPs had wanted a conscience vote but the caucus had decided to opposed it unless changes were made to exempt parents from the provisions.
Labour MPs on the select committee refused to make that change to the bill.
National leader Christopher Luxon said he "fully" supported the legislation, and anticipated the vast majority of his MPs would too.
"I am a proud supporter of the LGBTQI+ community. I want New Zealand to be a country that celebrates and supports diversity, including our rainbow community.
"There will be those with different views for different reasons across Parliament.
"These sorts of issues are traditionally treated as conscience issues, and we determined as a caucus that this was the appropriate course in this instance."
National Party deputy leader Nicola Willis said she would also support it.
Simon Bridges, who was justice spokesman when the party first decided to oppose it, said he would vote against it unless changes were made once it returned to Parliament for amendment. That is unlikely to happen.
Justice spokesman Paul Goldsmith said he did not support conversion therapy, but had concerns with elements of the bill. He would see what changes were made by Parliament before making a decision.
While Act supported the bill at its first reading the party said it retained "serious concerns" about its potential to criminalise parents, particularly around stopping their own child taking puberty-blockers.
In the report the party indicated it would not support the bill, with concerns including how parents could be prosecuted for having a conversation with their children about puberty blockers, and around free speech for parents and religious institutions.
Seymour said he had earlier flagged concerns about whether there was a need for the legislation, and whether it would impact on parents' abilities to have conversations with their children. It was unlikely Act would continue to support it, but the caucus would discuss it on Tuesday, he said.
The bill creates two new criminal offences for either the most serious cases of harm or where there is heightened risk of harm. The bill also creates a pathway for civil redress.
Under the bill, it will be an offence to perform conversion practices on a child or young person aged under 18, or on someone with impaired decision-making capacity. Such offences would be subject to up to three years imprisonment.
There were nearly 107,000 submissions on the bill, majority form submissions but nearly 40,000 unique. There were 837 oral submissions over 18 hearings.
The committee proposed several amendments to wording in the bill, which will be reported back to the House during its second reading.
