A Stormont private members bill brought by Paul Givan aims to prevent abortions from being carried out in cases of non-fatal disabilities.
Significant changes to the law came into effect last year following legislation passed by Westminster MPs while Stormont was collapsed.
Abortion had only been allowed in a very limited set of circumstances before then.
Under the new laws, there is no time limit for terminations when there is a substantial risk a fetus would suffer severe mental or physical impairment, such as Down's syndrome.
The bill by Mr Givan, MLA for Lagan Valley, a constituency near Belfast, aims to amend this part of the law.
It is the first attempt by an MLA to change NI's abortion laws since the Assembly was restored in January last year.
According to Mr Givan, the bill does not seek to affect a provision within the law that permits abortions up to birth for fatal foetal abnormalities, where babies are not expected to survive outside the womb.
The proposed change is being backed by disability rights campaign group Don't Screen Us Out, which claims the law is discriminatory and will allow abortions without time limit for conditions such as Down's syndrome or cleft palate.
One high-profile activist involved in the campaign is Heidi Crowter, who has Down's syndrome.
Ms Crowter is also taking separate legal action against the UK government against a similar element in the 1967 Abortion Act, which applies in Great Britain.
Mr Givan said he worked with other parties on the bill, which is due to get its first reading in Stormont on Tuesday.
If the bill gets a second reading and a majority of MLA support it, then it will go to the committee stage for scrutiny.
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