Gerry Adams has called for a general election
Taoiseach Enda Kenny has stepped down as Fine Gael leader.
He says he will continue his duties as Taoiseach in an acting capacity, until a successor is elected.
This process is to be completed no later than June 2nd, he says.
One of the favourites to succeed Mr Kenny as leader, Social Protection Minister Leo Varadkar, said he "brought Fine Gael from the edge of extinction to its current position".
"Enda Kenny has been an extraordinary Taoiseach and Fine Gael's most successful leader ever. After decades of service to our Party and country, we owe him a debt of gratitude", he says.
Those from across the political spectrum have also paid tribute.
Housing Minister Simon Coveney said Mr Kenny "has been a towering figure in modern Irish history" and that he will be recognised as such.
"With his vision, determination, positivity and relentless work-rate he led our party back from defeat and to sustained electoral success, culminating in victory in the 2011 general election and a record result for our party."
"I am proud to have served in opposition and then in Government with Enda.
"I saw at close quarters how skilled and driven he was to succeed for our party, in Government and for our country.
"His record in Government since 2011 will be viewed very positively by historians, not least how he led the restoration of our economic financial independence over that period, which was a landmark event."
British Prime Minister Theresa May said Mr Kenny "has been a strong and consistent friend to the UK".
PM: Enda Kenny has been a strong and consistent friend to the UK. I wish him all the very best for the future.— UK Prime Minister (@Number10gov) May 17, 2017
Former British Prime Minister David Cameron said Mr Kenny "was a strong leader for Ireland, a great partner for the UK, and remains a good friend."
.@EndaKennyTD was a strong leader for Ireland, a great partner for the UK, and remains a good friend.— David Cameron (@David_Cameron) May 17, 2017
The leader of Fianna Fáil Michael Martin said: "I wish to take this opportunity to pay tribute to the Taoiseach Enda Kenny for his contribution to Irish political life since his first election to Dáil Éireann in 1975, and particularly in his role as Taoiseach and leader of the Fine Gael party.
"One of the fundamental tenets of our democracy is a commitment to public service and the Taoiseach has more than fulfilled that obligation. He has worked diligently for his county, party and country over a long period of time.
"While over the years we have had our differences on many political and policy issues, I have always appreciated Enda’s decency, good humour and approachability".
The leader of the Labour Party, Brendan Howlin, said: "I believe that Enda Kenny will be remembered as Taoiseach of the Government that brought our country back from the brink.
"The period from 2011 to 2016 was a difficult time to hold public office in Ireland. But regardless of the challenges we faced, Enda Kenny took them on with humour, grace, and determination.
"He did his country much service, and I wish him the very best in the next chapter of his life."
Green Party leader Eamon Ryan TD said: "We'd like to thank Enda Kenny for his service as Taoiseach over the last six and a half years, and wish him well for the future.
"We commend him for stepping aside as leader of Fine Gael with a speedy process in place to have his successor selected by the 2nd of June.
"The Fine Gael leadership process must be immediately followed by the appointment of Enda Kenny’s successor as Fine Gael leader as the new Taoiseach ahead of the crucial European Council meeting of June 22nd, where items of critical importance to Ireland regarding the Brexit process will be discussed and decided."
Sinn Féin leader Gerry Adams said: "I would like to wish Enda Kenny, his wife Fionnuala, and their family well. It will be a big a change in all of their lives.
"He and I disagree on many political issues, but I acknowledge that he did his best from his perspective.
"From Sinn Féin’s perspective, this was not good enough.
"In 2011, Mr Kenny came to power with the largest majority in the history of the state. He promised a democratic revolution.
"Six years on and his political legacy is dominated by crisis, chaos, and chronic lack of accountability."
Mr Adams highlighted the ongoing housing and homelessness crisis, health service "chaos" and a "deep crisis in policing and justice".
"That will not change under Leo Varadkar, Simon Coveney or any other contender. We need a change of Government, not just a change of Taoiseach."
Jobs Minister Mary Mitchell O’Connor said Mr Kenny "has been a phenomenal Fine Gael leader, Taoiseach, politician and parliamentarian."
"He was one of the few, indeed maybe the only, politician who had the drive, the skillset and the courage to step up and do the work needed to secure our state. When needed most, he showed stamina, strength and conviction."
"The right person, for the right job, at the right time. We all owe him a debt of gratitude", she adds.
"His legacy is secure. A legacy of a man who never had, nor sought, universal popular approval but who showed political integrity and unwavering fortitude."
She also praised Mr Kenny for bringing down the unemployment rate from 15% when he took office to 6.2% now.
"The upcoming Fine Gael leadership contest needs to be about who best embodies the attributes and values that Fine Gael stands for. Who can continue our economic progress, in the right way. And who can continue our social progression."
Children's Minister Katherine Zappone said Mr Kenny "guided Irish politics during a huge period of social, economic and political change".
"As a leader he was always open to change, the successful Marriage Equality Referendum is the greatest example of this.
"Enda Kenny is at all times respectful and willing to listen to diverse views. It is a talent and a skill which will serve him well no matter what future path he takes."
"I wish Enda, Fionnuala and their family every good wish for the future.
"However it is also important in the coming weeks that our plans for children, young people and families are not stalled.
"As the only Independent woman in Cabinet I will continue to press on these and other issues."
The CEO of business group IBEC, Danny McCoy, said Mr Kenny represented Ireland "at home and abroad with great energy and dignity".
"His boundless positivity chimed with the innate optimism of the business community.
"He effortlessly won over audiences internationally, who were always impressed at his receptiveness to new ideas and his embrace of Ireland's open, global outlook.
"As a leader, he steered the country from the doldrums of the Troika to where we are today, a rapidly growing and internationally feted economy of substance."