Update 9.10pm: The Independent Alliance have referred to Enda Kenny as a true statesman and thanked him for his leadership of the minority Government.
They say during the Fine Gael election campaign the work of Government must continue.
And junior minister Finian McGrath says Leo Varadkar and Simon Coveney have assured him there won't be any snap election: "Actually I have talked to both of them about that issue, because that would have been a concern of the Independent Alliance.
"Both of the, both Simon and Leo, have said they would be very interested in sticking to the three year plan, implement as much as possible the progamme from Government."
Update 8.15pm: British Prime Minister Theresa May has wished Enda Kenny all the best describing him as a strong and consistent friend of Britain.
In a statement issued through the Number 10 Downing Street Twitter account, she said: "Enda Kenny has been a strong and consistent friend to the UK. I wish him all the very best for the future".
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 (@10DowningStreet) May 17, 2017
Update 7.30pm: The leader of the Labour Party Brendan Howlin has said Enda Kenny will be remembered as Taoiseach of the Government that brought our country back from the brink.
"He did his country much service, and I wish him the very best in the next chapter of his life."
Update 6.45pm: The former Tánaiste, and Minister for Social Protection Joan Burton has said Enda Kenny's demeanour and physical fitness helped him to carry out his duties work as Taoiseach.
Speaking on RTÉ's Drivetime Ms Burton said Mr Kenny would often work 14-15 hours per day, but that this came easy to him largely because he was very physically fit.
She said he had it in his capacity to be serious but 'he was also able to be relaxed in the midst of challenges, at a very tense time in the country's history.'
Ms Burton said, in her view, the failure of health reforms to show dividends was one of the most frustrating issues for Enda Kenny during his time in office.
Update 6.30pm: Green Party leader Eamon Ryan has commended Enda Kenny for stepping aside as leader with a 'speedy process'
On behalf of the Green Party, Mr Ryan thanked Mr Kenny for his service as Taoiseach and wished him well for the future.
Update 6.10pm: The leader of Fianna Fáil Micheál Martin has paid tribute to Enda Kenny as he steps down as leader of the Fine Gael party.
He said although they have had their differences, he always appreciated "Enda's decency, good humour and approachability."
Micheal Martin statement pic.twitter.com/k6DRMTUoym— Gavan Reilly (@gavreilly) May 17, 2017
Mr Martin wished Mr Kenny well and thanked him, on behalf of the the Fianna Fáil party, for his years of public service.
Fine Gael deputy leader Dr James Reilly said: "I think Enda Kenny has proved himself to be one of the outstanding politicians of this century and the last."
Update 6pm: The process of replacing Enda Kenny as Fine Gael leader will be finalised tomorrow.
The party's National Executive Council is expected to back the recommendation for it to be all over before the June Bank Holiday weekend.
Parliamentary Party Chairman Martin Heydon says it'll take a bit longer before the new leader becomes Taoiseach: "If we have the election of a new leader on June 2, the Dáil is not due to sit the following week.
"And it is Dáil Eireann which will elect a new Taoiseach, not the Fine Gael party, so there wouldn't be an opportuniy for over a week.
"If any new leader is appointed they will have a lot of people to talk to, we have a number of partners in Government and we have a number of other people who we have partnerships in the Dáil."
Update 5.45pm: Leo Varadkar has released a statement full of praise for Enda Kenny, following the announcement that he will retire from his position as Leader of the Fine Gael Party.
In the statement, Mr Varadkar said:"Enda Kenny has been an extraordinary Taoiseach and Fine Gael’s most successful leader ever."
The Minister for Social Protection said his party and the country "owed him a debt of gratitude."
He went on to say when elected in 2002 he brought renewal and hope.
The statement which is full of positive remarks outlines Mr Kenny's treatment of Leo Varadkar.
"On a personal level, I owe him so much. He appointed me to the Party’s Front Bench following my first election as a TD. I was honoured to accept a Ministerial position from him after the 2011 election. I have learned a lot from Enda, in particular how to lead a team of people with many talents and diverse views."
He finishes off the statement by saying "he was a kind and decent man... I know that the party and the country, will always remember him and will always be grateful."
Update 5.20pm: Sinn Féin President Gerry Adams has wished Enda Kenny and his family well in his retirement from his position as leader of the Fine Gael party.
In a statement, Mr Adams said: "“He and I disagree on many political issues, but I acknowledge that he did his best from his perspective."
Gerry Adams comments on Enda Kenny announcement https://t.co/RmjW3gIrPm— Gerry Adams (@GerryAdamsSF) May 17, 2017
He followed this rather flattering line with a sharp comment that disintergrated any pleasantries: “From Sinn Féin’s perspective, this was not good enough."
The statement then goes on to list Mr Kenny's 'failings' in the eyes of the Sinn Féin leader:
"“Six years on and his political legacy is dominated by crisis, chaos, and chronic lack of accountability.
“There is an ongoing and unprecedented crisis in housing and homelessness…"
Before moving on to a stab at the Fine Gael Party in general: “The reality is that Fine Gael, no matter who leads them, are firmly wedded to the policies that cause so much hardship in the daily lives of ordinary people.
“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.”
Update: 5pm: Taoiseach Enda Kenny has announced his intention to retire as leader of Fine Gael effective from midnight tonight, writes Daniel McConnell.
Mr Kenny has addressed the Fine Gael parliamentary party a short time ago and is said to be “quite emotional”.
The meeting is said to have lasted less than fifteen minutes.
In a statement on his Twitter account, Mr Kenny said he was honoured and privileged to have served as leader since 2002.
His statement said: “I have decided to implement that decision today.
Therefore, I will retire as leader of Fine Gael effective from midnight tonight.
I will continue to carry out my duties as party leader in an acting capacity until my successor is elected through the Fine Gael election process.
I have asked that the FG executive council expedite this process and to have it concluded by close of business Friday June 2nd.
I want to assure people that throughout this internal process, I will continue to carry out my duties and responsibilities as Taoiseach in full.
I intend to provide a brief but appropriate period for my successor to engage with groups and members supportive of Government, and with other parties in the Dail regarding of the provision of Government for the future.
I would like to stress the huge honour and privilege it has been for me to lead our party for the past 15 years, in Opposition and into government on two successive occasions.
I thank all our members, past and present for that privilege.
I thank all my loyal constituents and supporters in Mayo for their unstinting loyalty since 1975 and for their support for my family previously in providing unbroken service to the county in Dail Eireann since 1954.
I thank my personal staff for their commitment over many years to their duties.
I especially want to thank my wife Fionnuala, our children, my siblings and their families for their understanding of my work, and indeed for accepting the many intrusions of politics into family life in the interests of building our country.
I could not have engaged as I did without that base. Thank you.”
Meanwhile, Fine Gael officials are preparing plans for a shorter 16-day campaign in order to conclude the leadership contest by the June bank holiday weekend.
It comes as the Irish Examiner has learned that the four regional hustings will be broadcast live on Facebook.
The party's national executive will meet today to formally move to open the process for nominations to be accepted.
This window for nominations will last for three days so that means nominations will close Saturday evening.
It will require 10% of the parliamentary party or 8 TDs, senators or MEPs to nominate a candidate.
Then a series of regional hustings will take place around the country.
Those hustings will take place in Dublin, Cork, Galway and somewhere in the midlands will begin towards the end of next week.
Update 4.44pm: Enda Kenny has announced he is stepping down from his role as Fine Gael Party Leader.
The news was announced on Twitter this evening and his retirement will commence at midnight tonight.
In the statement, released on Twitter, Mr Kenny said he would remain in the role of party leader for Fine Gael in an acting capacity until a successor has been chosen.
He will continue to carry out his duties as Taoiseach in full.
Enda Kenny has also asking for the election of his successor to be expedited and announced by June 2.
Tributes to Mr Kenny have started to roll in on the social media network as people remember his work as Party Leader of Fine Gael.
Mr Kenny went on to say what an honour and a privilege it had been to lead the Fine Gael Party for 15 years.
Earlier: Taoiseach Enda Kenny has brought forward the Fine Gael parliamentary party meeting to 4.30pm amid an imminent announcement over his future, writes Fiachra O Cionnaith, Irish Examiner Political Correspondent.
The early meeting for the private event, which is usually held on Wednesday evenings, was confirmed to Fine Gael TDs, senators and MEPs a short time ago.
The email, seen by the Irish Examiner, states that at the request of Mr Kenny the meeting will begin at 4.30pm.
While it gives no explanation as to the move, the schedule change is widely expected to relate to an imminent announcement about Mr Kenny's future.
The Taoiseach last week told the parliamentary party meeting he would make his future plans clear at today's meeting.
It is widely expected - although not yet confirmed - Mr Kenny will tell today's meeting he will step down by the end of next month, with a leadership contest in early June.
Housing Minister Simon Coveney and Social Protection Minister Leo Varadkar are certain to officially launch leadership campaigns within days, with Education Minister Richard Bruton and under-fire Justice Minister Frances Fitzgerald also considering leadership bids.