The 33rd Dail has sat for the first time some 11 days after the outcome of the general election produced a different political landscape.
The 160 TDs gathered at Leinster House where all their names were read into the record by the Clerk of the Dail Eireann.
Procedures got under way at noon with Clerk Peter Finnegan reading out the Proclamation.
Fianna Fail TD Sean O Fearghail was re-elected as Ceann Comhairle in the Dail after receiving 130 votes.
He beat Independent TD Denis Naughten who received 28 votes.
He was elected following a secret ballot.
Mr Naughten was the first to make his pitch for the role.
He cited his experience as a parliamentarian at all levels, from TD to cabinet minister.
Mr Naughten said there is “public frustration” over accountability in public services.
“Getting straight answers to straight questions has become very difficult in Dail Eireann,” he said.
Before he was elected, Mr O Fearghail told the Dail that he was seeking a renewal of their support for the role.
“I work in the basic principle of respect for the mandate that each member of the Dail has received from their electorate,” he said.
“That mandate is in every respect equal and deserving of similar priority.”
Ballot papers were given to TDs with the secret ballot taking place in the voting lobbies in specially constructed booths.
During the first sitting, the Dail failed to elect a taoiseach.
Sinn Fein leader Mary Lou McDonald, Fianna Fail leader Micheal Martin, Fine Gael leader Leo Varadkar and Eamon Ryan were all nominated for the role, however none of the leaders emerged with a majority vote.
Ms McDonald emerged as the most popular candidate with 45 TDs backing her.
However, 84 TDs voted in opposition with 29 TDs abstaining.
Mr Varadkar secured 36 votes in favour of him becoming taoiseach, while 107 TDs voted in opposition.
Mr Martin secured 41 votes in support, with 97 TDs voting against him.
Mr Ryan received 12 votes in support and 115 votes in opposition.
Mr Varadkar later travelled to see President Michael D Higgins at his official residence at Aras an Uachtarain to resign from office, however he will continue to carry out his duties as Taoiseach in a caretaker capacity until a new taoiseach is appointed.
He told the Dail: “The responsibility is on all of us to ensure we provide good government, and indeed good opposition.
“I think the onus is on those who have made enormous promises of change to the people during this election who are entrusted with that mandate to bring a programme of government for approval.
“If they cannot, they should say so and be upfront and honest about their failures and the empty promises they made.”
He said he will travel to Washington DC for the traditional St Patrick’s Day events.
Mr Martin accused Sinn Fein leader Mary Lou McDonald of using “populist tropes” as she accused them of failing to speak to her in government formation talks.
“Every party and deputy elected to this house has a right and a duty to represent the mandate they received. In order to deliver functioning government, compromises have to be made and this is something we have been attacked for.
“Demanding that others stay quiet as others abandon their core beliefs in order to grab power is notsomething we agree with.
“Whether or not you agree with Fianna Fail, we fought this election based on a clear set of principles and policies and that includes legitimate behaviour in a democratic republic.”
Mr Martin says he rejects Sinn Fein’s manifesto promises of increasing taxes on businesses and too many incompatibilities exist between the two parties.
Ms McDonald told the Dail: “Today for the first time a nominee other than Fianna Fail or Fine Gael has garnered the greatest number of votes. Perhaps that makes us winners again.
“I still we still live rent free in Micheal Martin’s narrow and bitter mind.
“Change means a secure roof over people’s heads, not having their adult children living in the box rooms.
“Change means you know you have enough to get by. Changes means dealing with the climate emergency. Change means the old order must pass.
“A vote for Sinn Fein was for a different government that would have the courage and energy to actually do things differently.”