The Stormont executive will have a "full discussion" about how abortion services should be provided in NI, First Minister Arlene Foster has said.
Major changes to NI's abortion laws came into force at the end of March.
However, the Department of Health has yet to put the regulations into practice.
The UK government said women from NI could continue to access services in England, but the Covid-19 crisis has led to restrictions on travel.
There have been calls for home abortions - in the first 10 weeks of pregnancy - to be permitted with doctors providing telemedicine services during the outbreak.
The provision has already been put in place in England, Scotland and Wales.
BBC News NI understands the NI executive discussed the issue at its meeting on Monday, but Stormont sources said it had led to a row between the parties.
Speaking at the Stormont executive's daily press conference about the coronavirus crisis, DUP leader Arlene Foster, whose party is strongly opposed to abortion, said ministers needed to have a full discussion about what should happen.
"The health minister will bring papers forward and we will have discussions, but I don't think it's any secret I don't believe abortion on demand should be available in NI - it's a retrograde step for our society," added the first minister.
"Instead of supporting people who find themselves in crisis pregnancies, we're not even having a discussion around that and how we can support people in those circumstances."
However, Sinn Féin Vice-president Michelle O'Neill said she supported extending telemedicine services to Northern Ireland during the Covid-19 emergency.
"We're talking about responding to a woman's need at time of the Covid-19 crisis, women shouldn't be left out," said the deputy first minister.
"This is about compassionate healthcare and making sure there's support for women who find themselves in vulnerable situations."
Ms O'Neill added that there was an obligation on the Health Minister Robin Swann to implement the new legislation and ensure there was provision in place in Northern Ireland.
The law changes were put in place by the Northern Ireland Office and took effect last week.
However the legal framework has not been implemented by Stormont's Department of Health yet and the Northern Ireland Office (NIO) had said until this happens, women could continue to travel to England, as journeys for medical need count as essential travel.
What is in the new framework?
Terminations will be legal up to 12 weeks without conditions.
A limit of 24 weeks will apply in situations where continuing the pregnancy would involve risk of injury to the woman's physical or mental health.
No time limit will apply in cases of fatal fetal abnormality, where there is a substantial risk that the fetus would die or, if born, would suffer a severe mental or physical impairment.
There will also be no time limit for an abortion if there is a risk to the life of the mother, greater than if the pregnancy is not terminated - or, the government says, "where necessary to prevent grave permanent injury to the physical or mental health of the pregnant woman or girl, including in cases of immediate necessity".
Medical professionals who can perform an abortion include a doctor, a registered nurse or a registered midwife.
Conscientious objection will apply - meaning those medical professionals who do not want to participate in carrying out a termination will not be obliged to do so.
The framework makes provision for abortions to be carried out in GP premises, clinics provided by a health and social care trust and HSC hospitals.
How did we get here?
Last July, MPs at Westminster voted to decriminalise abortion in Northern Ireland and create new laws.
Prior to that vote, abortion was only allowed in very limited circumstances.
It fell to the NIO to come up with a framework to oversee the provision for abortion services.
Last week, the regulations were made public for the first time and set out when and where abortions could take place, as well as who could carry them out.