Social Democrats TD Jennifer Whitmore has criticised what her party has said is a lack of women in the new Cabinet.
Of the 15 new Cabinet ministers, three are women, a figure that increases to four when Chief Whip Mary Butler is included.
In a statement, Deputy Whitmore said: "It is deeply disappointing that the number of women in Cabinet has reduced by 25% to just three.
"There are now as many men named James in the Cabinet as there are women.
"Fianna Fáil and Fine Gael pay lip service to increasing women's representation in politics. They just don’t believe in promoting them when they get elected.
Ms Whitmore said the Dáil has the worst gender balance of parliaments in western Europe, with women making up only 25% of TDs.
She said that instead of working to address that, by promoting talented women from within their own ranks, the "Government parties have reverted to type - creating a cosy boys’ club".
Meanwhile, a Fianna Fáil councillor has also criticised the low number of women in Cabinet describing it as a "backward step".
Cllr Rachael Batten who is the Fianna Fáil group leader in Dublin City Council said she believed women had been "sidelined" in the current Cabinet and she called for urgent action to address the issue.
"As a woman in politics, and as a mother, I find it difficult to accept that we continue to tell our daughters that there is an equal playing field in politics when the evidence stands in stark contradiction.
"We need stronger policies and leadership that reflect the realities faced by women in society and create the conditions for true gender equality in our political institutions."
Concerns over Government priorities
Unaligned Independent TDs in opposition have criticised the make-up of the new Cabinet and said they have concerns over its priorities.
Speaking in the Dáil this evening, Independent TD for Donegal and 100% Mica Group member Charles Ward, said he is from a constituency with a Red weather warning where people "can't stay in their houses" due to the Mica controversy.
He said people in Donegal are "in a humanitarian crisis" due to "Weetabix houses", and that the north west cannot be forgotten by those in power.
Independent TD and former Sinn Féin member Brian Stanley told the Dáil that in his view "we have a new Government of two old parties and one Regional group".
He said "the two civil war parties are united like never before, nothing separates them except one letter - FF and FG", and that "the big issues" facing people such as rent prices are not being addressed.
Unaligned Independent TD Catherine Connolly also criticised the new Government's formation, saying she is "seriously concerned you have utterly failed to recognise" what she said are in her view some of the biggest issues in society.
Deputy Connolly said in her view the Programme for Government "smacks a little bit of artificial intelligence", saying it is "very vague and aspirational" on some issues and "very specific on the triple lock".
Ms Connolly also said that she is "ashamed to stand here [in the Dáil] today with 15,000 people homeless", and called on the new Government to take action on the matter immediately.
Additional reporting Samantha Libreri
