South Down Sinn Féin MLA Caitríona Ruane stated that the petition has been submitted by Sinn Féin and MLAs from the Alliance and Green Parties in relation to a DUP and SDLP proposal.
DUP and SDLP MLAs jointly tabled an amendment last week to make it illegal to carry out terminations other than on Health and Social Care Trust premises.
It is due to be debated in the assembly on Tuesday, but it now cannot be passed unless it receives cross-community support.
Ms Ruane said the proposed change undermines a pregnant woman's ability to receive emergency treatment in life threatening circumstances.
"Sinn Féin is not in favour of abortion. We opposed and voted against the extension of the 1967 Act to the north when it was proposed in the Assembly," she explained.
"However, in circumstances where a pregnant woman's life is in danger we believe that the option of termination should be available."
This amendment, which was introduced at the last minute, is not about protecting women's health, it is about undermining a pregnant women's ability to receive emergency treatment in life threatening circumstances.
Caitríona Ruane, SF MLA
She continued: "We approach this complex issue with compassion and understanding and respect, conscious of strong and sincere views held on all sides and we hope that tomorrow's debate will be conducted in this manner."
Green MLA Steven Agnew said the amendment was ambiguous and unclear.
"The Petition of Concern was designed to stop the majority of the House forcing its will on the minority," he commented.
"Given less than 20 per cent of the Assembly is female, while 50 per cent of the general population in Northern Ireland are women, my opposition to this amendment is about protecting women's equality."
He added: "Tagging legislation which really needs public consultation on to the end of the Criminal Justice Bill is also a bad way to legislate
"It has taken 12 years to even get guidelines on access to terminations and as soon as they are published, we get an ill-considered, knee-jerk amendment which could lead to further delay in women accessing the treatment they are legally entitled to."
Pro-life campaigner Bernadette Smyth said the move was "an abuse of the democratic process".
"We have elected our politicians here and we believe that it would be political suicide for Sinn Féin if they oppose this, it's important that we debate this issue," she said.
I think it’s important that all people in Northern Ireland are represented, and I think it’s important that Sinn Féin allows the democratic process to go forth.
Bernadette Smyth, Pro-life campaigner
On Friday Justice Minister David Ford said he would oppose the move, stating that "tacking on a last-minute amendment" to the bill was not the way to deal with the issue.
He said the wording of the amendment "could lead to overlapping offences and confusion in an area where clarity is needed".
The amendment was initially raised by DUP MLA Paul Givan and the SDLP's Alban Maginness, who have raised concerns about private sexual health care clinics.
The MLAs have expressed concern regarding the transparency, accountability and oversight of a Marie Stopes Clinic in Belfast, which offers medical abortions within the scope of NI law, as well as a range of sexual health services.
Under current legislation, abortion is illegal in Northern Ireland except in limited circumstances where the mother's life or mental well-being is considered at risk.
DUP Health Minister Edwin Poots has previously said he supports the amendment, and that regulation of abortion was best "done under criminal justice law".
Mr Poots has circulated draft guidelines on how and when terminations can be carried out to the Northern Ireland Executive.
It is understood these proposals include the specification that two doctors should be contacted for mental health assessments when considering the procedure.