The Taoiseach has wished Arlene Foster "the very best" for the future, following her announcement that she would step down as leader of the DUP and as First Minister of Northern Ireland.
Micheál Martin said Mrs Foster has "worked hard over many years" as an elected representative for her constituency.
He said political leadership is "often not easy", and Mrs Foster "sent a strong message to women about what can be achieved in and through politics" as the first female leader of the DUP and the first female First Minister of Northern Ireland.
The Taoiseach said that he spoke to DUP leader Arlene Foster earlier today to wish her well. Micheál Martin said that on a personal level it is a difficult time for her. | Read more: https://t.co/pFhDtBlDPb pic.twitter.com/b5asENth0Y— RTÉ News (@rtenews) April 28, 2021
"She has served during what has been a period of considerable change and challenge in Northern Ireland", Mr Martin said.
"The re-establishment of the Northern Ireland Executive in January 2020 with Arlene Foster as First Minister and Michelle O'Neill as Deputy First Minister was a key development in supporting peace and stability for all the people of these islands.
"The Northern Ireland Executive under their leadership has had to grapple with the Covid pandemic almost since the beginning, and I pay tribute to Arlene's role in guiding Northern Ireland through this challenging period."
Mr Martin said that despite their differences, he "valued the constructive engagement ... we have had in our respective roles as Taoiseach and First Minister".
Arlene Foster has announced she will step down as leader of the Democratic Unionist Party and First Minister of Northern Ireland. | Read more: https://t.co/pFhDtBlDPb pic.twitter.com/6CdMR10pLu— RTÉ News (@rtenews) April 28, 2021
Tánaiste Leo Varadkar said he was sorry to see that Arlene Foster had resigned, saying it demonstrated how brutal politics can be.
Mr Varadkar said he knew Arlene Foster very well, having worked with her when they were both Tourism Ministers and more recently as leaders of their respective parties.
He said that the DUP should be given time and space to elect a new leader.
"Serving in public life makes great demands on individuals, which is important to acknowledge.— President of Ireland (@PresidentIRL) April 28, 2021
May I thank Arlene Foster for her public service over many years and wish her health and happiness in the future."
Northern Ireland's Deputy First Minister has also wished Arlene Foster well, and said Mrs Foster had contacted her earlier to inform her she would be stepping down.
"I wish Arlene and her family the very best for whatever the future may hold," Michelle O'Neill said.
"I've worked very closely with her for the past year. We have led together through this pandemic and I acknowledge her work in working with Executive colleagues in what had probably been one of the biggest challenges of our generation in terms of our political leadership."
Sinn Féin's Michelle O’Neill said she and Arlene Foster have worked together very closely over the past year. She said she hopes any incoming leader will be committed to power-sharing and working together. | Read more: https://t.co/pFhDtBlDPb pic.twitter.com/kHuH2pXX72— RTÉ News (@rtenews) April 28, 2021
Ms O'Neill said the incoming DUP leader "should recognise that the political landscape across our island has changed".
When asked about who might succeed Mrs Foster, she said: "I'll not offer a preference."
"I'm a joint head of government", she said. "I will work with all political parties around the executive table to make politics work and power sharing has to work for every single person who we all collectively represent".
Ms O'Neill said she and Arlene Foster will continue to work together until the end of June, and she hopes that the new DUP leader will want to "work together with all political leaders to make politics work".
Sinn Féin leader Mary Lou McDonald said today is "undoubtedly a difficult day" for Arlene Foster.
She said Sinn Féin wants to work with the incoming DUP leader "in a spirit of generosity and respect", which she said means having partners who are "committed to and willing to share power with the other four parties in the Executive, and with the Irish Government in the North-South Ministerial Council".
Ms McDonald said unionism is "at a crossroads" now.
"The inbuilt unionist majority is now a thing of the past", she said.
"Progressive social changes such as marriage equality are happening. Brexit and Covid-19 are also driving the politics of change.
"There is no going back."
Sending @DUPleader Arlene Foster and her family personal good wishes.— Colum Eastwood (@columeastwood) April 28, 2021
Regardless of personnel changes – the fundamental problems haven't changed, and neither have the solutions. Those who want to take her place need to reflect on how we work together to unite our communities.
The DUP's Jim Wells has said it would be wrong to say that Mrs Foster's abstention on the conversion therapy vote was a catalyst. He said that it "was one of many, many issues - maybe the straw that broke the camel's back".
Speaking on RTÉ's Drivetime, he said there has been huge concern about the way the party was going over the last 18 months and this brought it to a crescendo.
He said the concern had been mounting since Christmas onwards.
"It would be wrong to say it was conversion therapy," he said. "It was the whole issue of the Protocol and perhaps personalities as well, there were many difficulties between the leadership and the ordinary grass roots."
He said "part of Arlene's problem was that many saw what she was doing as too progressive and taking the province and the party too far."
Meanwhile, the leader of the Social Democratic and Labour Party said the circumstances that led to Mrs Foster stepping down are "deeply concerning".
In a statement this afternoon, Colum Eastwood said it is "distressing" that a political leader would be removed from office by their party for "failing to support conversion therapy".
This will "cause some alarm for members of our LGBT+ community", he said.
"They should know that we will not roll back on the progress we've made or deny them their rights."
Mr Eastwood said they need parties and political leaders "who are committed to the institutions of devolution and want to make this place work".
He said that while he and Mrs Foster "disagree on almost everything", she has "clearly been a committed servant to her party".
Best wishes to @dupleader Arlene Foster & her family this evening. While we bring different perspectives to some issues, she has worked sincerely, tirelessly & with determination for her party & for NI as First Minister.— Simon Coveney (@simoncoveney) April 28, 2021
Minister for Foreign Affairs Simon Coveney wished Arlene Foster and her family well.
He said that while they have "different perspectives" on some issues, she has "worked sincerely, tirelessly and with determination" for the DUP and for Northern Ireland.
I wish her all the best and look forward to continuing to work with her in the days and weeks ahead, delivering for all the people of NI.— Brandon Lewis (@BrandonLewis) April 28, 2021
Secretary of State for Northern Ireland Brandon Lewis tweeted that Mrs Foster is a "truly dedicated public servant" who devoted her political career to her constituents.
On Twitter, he said: "There are many young people, particularly young women, who will be inspired by her example to follow a path into politics.
"I wish her all the best and look forward to continuing to work with her in the days and weeks ahead, delivering for all the people of NI."
British Prime Minister Boris Johnson thanked Mrs Foster for her "dedication to the people of Northern Ireland".
He said she will continue to play a "vital role" as First Minister until the end of June, and he hopes she remains in public service.
I want to thank Arlene Foster @DUPleader for her dedication to the people of Northern Ireland over many years. She will continue to play a vital role as First Minister until June and I hope that she stays in public service for years to come.— Boris Johnson (@BorisJohnson) April 28, 2021
Former taoiseach Bertie Ahern has said he hopes that the new leader of the DUP will take a positive looking, progressive stance on issues and that they will look at a relationship with the Republic and lead in a progressive way.
He said there are plenty of mechanisms in the Northern Ireland Protocol for trying to deal with issues, which have created problems with trade not just in Northern Ireland but also in the Republic.
However, he said there are positives as Northern Ireland is still in the customs union and the single market and it has significant economic benefits now over other places.
Mr Ahern said he has known Mrs Foster for a long time and on a personal level he found her very friendly and kind. He said she had given a lot of good service in a lot of key ministries.
Additional reporting by Laura Hogan