Sinn Féin is ready for opposition and will "continue to fight for change", the party says.
Despite receiving the highest number of first preference votes in February's election, Mary Lou McDonald's party will now lead the opposition in the Dáil. Finance spokesman Pearse Doherty said that the Fianna Fáil-Fine Gael coalition represented a "circling of the wagons" by the Civil War parties.
"People voted for change in the general election, they voted for a fresh start and for a new beginning. They voted for a move away from the two parties that have shared power in this State for nearly one hundred years.
"Faced with the prospect of a Government of Change, the two old parties have come together to circle the wagons to exclude Sinn Féin, and they are using the Green Party as a fig leaf to do this.
"The reality is that the desire for change is even stronger now than it was in February. People know what it's like to have Fianna Fáil and Fine Gael in power together."
Sinn Féin sources had indicated that the party would introduce the Occupied Territories Bill, which would ban trade with occupied settlements in Israel, in the early days of the government. This could require Fianna Fáil and Green Party members to vote against a bill which they have previously supported. Party housing spokesperson Eoin O Broin said the move could happen within months.
There has been mounting speculation that Sinn Fein will table the Occupied Territories Bill in the first six months of the new government.
"I'm not so sure the people of Palestine can wait six months," Mr O'Broin said, who added it was "hard to say" how long the proposed government would last.
"I think once we successfully exit out of COVID-19 and that hasn't happened yet, I do think the public's concern is going to shift.
"I think once those issues of (housing and healthcare) bubble back up to the top of the political agenda, then if a government isn't dealing with those in an adequate way, that government is going to be short-lived, and if you consider the number of spats that we've heard between the three over the last number of weeks, if they're already at each other's throats before the government is formed.
"What's going to happen afterwards?"
Meanwhile, People Before Profit TD Richard Boyd Barrett said that the approval of the deal paved the way for "more of the same".
“In voting for this Programme for Government the Green party have, in effect, given the green light to maintain the status quo rather than to bring about the change people voted for in the general election."