If re-elected, Labour says it will reform surrogacy laws to "ensure rainbow people who want to form a family are treated on an equal basis as heterosexual couples".
The party also wants to establish a rainbow refugee sub-quota and look at removing restrictions on men who have sex with men from giving blood.
The promises - among others - were made in Labour's Rainbow Manifesto, released on Saturday afternoon.
"The Labour Party has a long history of being relentlessly proud and fighting alongside rainbow whānau for equality and justice, and I will continue that when re-elected," leader Chris Hipkins said.
"While other parties are using members of our rainbow communities to incite fear and division this election, we are laying out our ongoing commitments to progress for our rainbow whānau.
"All people, including rainbow communities, deserve to have their rights and dignity upheld, and to live their lives freely just as they are."
Labour said it wanted to "reform adoption laws, in line with proposals in the 2022 discussion document 'A new adoption system for Aotearoa New Zealand'" and "pass the Improving Arrangements for Surrogacy Bill, in response to the recommendations in the Law Commission report 'Te Kōpū Whāngai: He Arotake Review of Surrogacy'".
"Currently, rainbow families are required to adopt their own genetic children after a surrogate birth - requiring court orders, interviews, and home visits to determine suitability," Hipkins explained.
"We will also establish a rainbow subcategory within New Zealand's annual refugee quota to support people who are being persecuted because of their sexuality or gender identity to resettle in Aotearoa New Zealand. Rainbow refugees can face additional barriers, exclusion, and discrimination compared to other refugees."
Labour would also continue to roll out the HIV Action Plan "which ensures communities at greater risk can access PrEP", the manifesto said.
PrEP is a drug that reduces the likelihood of transmission of the virus by 99 percent.
The party promised to form a "blood donation roundtable, bringing together advocates, experts and specialist organisations to explore the latest evidence" around the three-month stand-down period men who have sex with men currently face before they can donate.
"Any change will need a strong guarantee of safety, but countries like Canada and Ireland have changed their rules, so we should look at their evidence," Hipkins said.
Labour will also "implement a child rights-based healthcare protocol for intersex children, so that no one is subjected to unnecessary medical or surgical treatment during infancy or childhood, and binary gender assignment is not automatically presumed to be the best-case outcome".
As for schools, Labour planned to encourage schools to adopt the Ministry of Education's sexuality education guidelines for principals, Boards of Trustees, and teachers, which "outline how schools should go about teaching to support the inclusion and wellbeing of students with diverse sexual orientations, gender identities and expressions, and sex characteristics".
The health curriculum's section on relationships and sexuality would also be up for review, the party said, in 2024.
Hipkins talked up Labour's recent record in advancing LGBTQ+ rights, such as giving "agency to people over their own identity" by making it easier for birth certificates to be updated to to "reflect how they identify" - whether that was transgender, non-binary, takatāpui and intersex, for example - and banning sexual orientation conversion practices.
"Living fully in your own skin isn't always easy for any of us at the best of times, and it can be particularly hard for our rainbow communities. I'm proud of our progress we've made to support our rainbow whānau and the commitments we're making."
The manifesto also noted the achievements of previous Labour-led governments, such as passing the Homosexual Law Reform Bill in 1986 and the Civil Union Act of 2004, as well as Louisa Wall's Marriage Equality Bill, which passed in 2013 in a conscience vote under a National-led government.
National leader Christopher Luxon said he wanted people to feel free to be themselves, talking up his track record as CEO of the national carrier.
"We respect the great diversity that's in [New Zealand]. We want to be a government for all New Zealanders, and all communities."
Most National MPs voted against legalising same-sex marriage in 2013, though some later said they had since changed their minds.
Almost all National MPs voted against legalising homosexual acts in 1986.
Asked about National's track record, Luxon pointed out his personal perspective.
"I look at my record at Air New Zealand, in terms of driving into a Rainbow Tick accredited employer, the work we did about helping people transition, all of those things, it's important to me that people are free to be who they want to be at work and in this community and they feel protected, safe and respected."
He said his view had always been in support of same-sex marriage.