The move comes as MLAs prepare  for an assembly debate on whether to make abortions legal in such cases.
A vote on whether or not to amend the Justice Bill is due to take place on Wednesday.
The proposed amendment looks unlikely to pass now that the DUP has said it will be voting against it.
Currently, a termination is only permitted in Northern Ireland if a woman's life is at risk or if there is a risk of permanent and serious damage to her mental or physical health.
Justice Minister David Ford has asked the executive to approve legislation for abortion in cases where a fatal foetal abnormality is diagnosed.
The DUP said the issue required proper consideration by the assembly and executive, and that the Bill was not intended for this purpose.
They have asked Health Minister Simon Hamilton to set up a working group, including clinicians and people with a legal background, to make recommendations as to how the issue can be addressed, including, if necessary, draft legislation.
It is to report within six months.
BBC News NI political correspondent Gareth Gordon said finding a way forward, which the majority of people can agree on, will be "a  mammoth task".
"This is one of the most sensitive issues facing politicians and society generally in Northern Ireland," he said.
In December, a High Court judge ruled the law does not comply with the European Convention on Human Rights in cases of fatal foetal abnormality or sexual crime.
The case was brought by the Northern Ireland Human Rights Commission.
The commission took legal action against Mr Ford's Department of Justice as part of its campaign for a change in the law.
In January, the justice minister said he was lodging an appeal to the ruling, because he was concerned that a lack of "legal certainty" could lead inadvertently to abortion on demand.
The DUP has asked the Northern Ireland health minister to set up a working group to look at how the issue of fatal foetal abnormality can be addressed.