Independent TD Catherine Connolly has asked Fianna Fáil members to vote for her in the presidential election, while Heather Humphreys has declined to say if she will meet the Taoiseach to seek Fianna Fáil's backing.
It follows Jim Gavin's withdrawal from the race over the issue of €3,300 he owed to a former tenant.
Speaking in Tallaght where she was campaigning, Ms Connolly said she wished Mr Gavin and his family "the best" and said it was very difficult for him.
"It's difficult, and the circumstances are very difficult and very difficult for the tenant who suffered," she said.
Ms Connolly said Fianna Fáil has a "proud history of backing neutrality".
She said the Government party had a chance to "reconnect" with voters and that she was "offering them that choice, and I'm very hopeful that they will now give their votes to me".
Ms Connolly said when she was elected as Leas Ceann Comhairle she "drew support from every side of the Dáil".
She said she has always picked up second and third preferences in elections and that she has "never had a difficulty attracting votes from different parties".
Asked if her strategy has changed with the race for Áras just between her and Heather Humphreys, Ms Connolly said she has had a specific strategy from day one.
"That was to stand up, announce my candidacy, and I made that decision after much reflection. I made it without thinking about the cost or having parties behind me. I'm very much an independent candidate," she added.
She went on to say this is a "very, very special election" and that it is particularly important to give people a choice.
Ms Connolly said she will "be a voice for peace, a voice to reflect positive neutrality, a voice that articulates the existential threat posed by climate change, and also a voice to reflect the essence of our community".
She said her campaign now has 12,500 volunteers and financial contributions from people ranging from €5 to €1,000. Ms Connolly described her campaign as "a movement".
"I'm the symbol of that movement, but this is historic where the parties have put aside their differences for the bigger vision for Ireland and for what's important. And I'm thrilled with that, and I will continue on with that strategy."
Watch: 'Difficult day' for Fianna Fáil says Humphreys
Ms Humphreys meanwhile declined to say whether she will meet the Taoiseach to seek the backing of Fianna Fáil for her election campaign.
Speaking to the media during a visit to Belfast, she was asked several times if she plans to meet Micheál Martin and to secure the formal backing of his party following Mr Gavin's withdrawal.
Ms Humphreys said she was seeking votes "from people right across the country".
"It's very early today, after that announcement last night, I have many Fianna Fáil friends, I really have, and you know, this is a difficult day for them," she added.
"These were the people that went out to put up posters, they've been out canvassing, they have been dropping leaflets, so I think it's important that we respect that, because it's not easy for them.
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"But look, I will want votes from everybody, because if I don't get enough number one votes, I won't get elected."
Pressed on whether she is seeking a meeting with the Taoiseach in the hope of securing his party's endorsement, she said that while she was grateful for Fine Gael's nomination, "the presidency is above party politics".
But she did not rule out the possibility of seeking Fianna Fáil endorsement.
"Micheál Martin is obviously very busy today," she said.
"This is a budget week, and I remember this time last year I'd have been in the middle of it. So look, as I said, I want votes from right across the board, and I hope people will judge me on my record and on my vision for the presidency."
