The Tánaiste Leo Varadkar has said the Irish Rugby Football Union shoud listen to the voices of those who are most affected by its updated Gender Participation Policy.
The IRFU said the decision was based on medical and scientific evidence and in line with World Rugby guidance, which last year banned transgender women players from competing at the elite level of the women's game.
A statement from the Department of Sport said the policy "recognises the complexity and sensitivity of this area as well as the concerns regarding safety within the sport".
It said it is important that the IRFU is committed to reviewing the matter on a continous basis and working directly with players affected by the policy and "the wider LGBT+ community".
"The emphasis on providing a range of opportunities for all players to remain involved is important too," it said.
It said Government ministers acknowledge "that this is a very complex and sensitive area and many sporting organisations are seeking guidance and support in developing their transgender policies".
"Sport Ireland is working with the sport sector to see how they can best support organisations," it said.
"That work is ongoing and Sport Ireland will continue to offer assistance and guidance to sporting organisations but ultimately it is the sporting organisations themselves that establish the rules and policies for their own sports," it added.
Meanwhile, a legal rights organisation has voiced "serious concerns" with the Irish Rugby Football Union's updated Gender Participation Policy.
Free Legal Advice Centres (FLAC) said the policy may give rise to unlwaful discrimination and serious human rights and equality concerns.
It said the policy "raises a number of concerns in relation to the human rights of trans participants in the activities of the IRFU, including their rights to privacy, data protection, dignity and bodily autonomy".
FLAC Managing Solicitor, Sinéad Lucey said the IRFU is subject to the Equal Status Acts which prohibits discrimination, including differences in treatment on the basis that someone is transgender.
"As a result, the exclusion of individuals from the sport on the basis of the new policy may give rise to discrimination complaints under the Equal Status Acts," she said.
While the Equal Status Acts allows for different treatment on the basis of gender in the context of sporting events, she said this exception only applies where the treatment can be shown to be reasonably necessary in the context of a given event.
"The exception, therefore, does not appear to permit a blanket policy of this kind which, by its nature, excludes an event-specific decision in relation to the participation of a trans person," Ms Lucey added.
FLAC, which is a member of Trans Equality Together, supported the call for the immediate suspension of the implementation of the policy.
Ireland captain Nichola Fryday was asked for comment on the new policy this afternoon, but says she will further educate herself on the topic before offering an opinion.