The party is opposed to terminations and has proposed a new law to prevent them being carried out in cases of non-fatal disabilities.
Sinn Fein will this week formally ask Stormont ministers to commission abortion services in Northern Ireland.
Party president Mary Lou McDonald accused the DUP and Ulster Unionists of blocking the change, two years after legislation was passed at Westminster.
Senior Democratic Unionist Paul Givan told the Stormont Assembly: “This bill is about tackling the attitudes and myths that lead to failures to provide high-quality support and care.”
He said discriminatory attitudes were still present.
“This is not something that our Assembly should tolerate.”
Northern Ireland’s previously restrictive laws were changed by MPs at Westminster in 2019 at a time when the Stormont administration was collapsed.
The laws allow abortion in all circumstances up to 12 weeks.
Terminations are permitted up to 24 weeks when there is a risk to the woman’s physical or mental health.
There is no time limit in cases of fatal foetal abnormality or when there has been a diagnosis of a serious physical or mental impairment that would cause a serious disability.
Abortions post 24 weeks in those circumstances are extremely rare.
Mr Givan said Downs syndrome life expectancy had increased to 50 or 60 years.
He lambasted the 2019 legislation.
“This sends out the message loud and clear that the lives of people with disabilities are less valuable and worthy of protection than the lives of people without disabilities, a law which fosters this thinking in 2021 is completely unacceptable.”
Individual health trusts have set up temporary early medical abortion pathways but Northern Ireland-wide services have not yet been commissioned by the Department of Health.
Minister Robin Swann has argued that, as a controversial issue, it is for the Executive to agree to set up the services.
Sinn Fein Communities Minister Deirdre Hargey is bringing forward a proposal to Stormont’s Executive this week to ensure services are delivered.
She said: “This is a crude attempt to roll back legislation in line with international human rights requirements.
“Despite this law being enacted to advance women’s health care it has not been implemented by the health minister.”