The Social Democrats will continue discussions with Fianna Fáil and Fine Gael around government formation next week the party has decided.
Deputy leader Cian O'Callaghan said he expects the party's five dealbreakers to come into focus when they meet with Micheál Martin and Simon Harris again.
With this in mind, it was decided that talks will also continue with Sinn Féin and Labour.
The negotiating team, made up of Mr O'Callaghan, Jennifer Whitmore and Gary Gannon, had met with the Fianna Fáil and Fine Gael ministers on Wednesday and updated the party this morning.
"We reported that the meetings had been positive and constructive with a good exchange of views," Mr O'Callaghan said.
He said there were detailed discussions with the two leaders around climate, housing, disability, healthcare and childcare.
The Social Democrats outlined its red-line issues during the campaign and said it intends to stand by these.
"Those dealbreakers were the delivery of 50,000 genuinely affordable homes during the lifetime of the next government; the full implementation of Sláintecare; quality public childcare; a senior minister for disability and credible climate action to avoid up to €20bn in EU fines," Mr O'Callaghan said.
He said there was "some interest" shown in the proposal to have a senior minister for disability.
"I wouldn't say it was rejected outright or anything like that but it was very initial discussions that we were having in those areas," Mr O'Callaghan said.
The most challenging topic of the discussions was in terms of climate, he said, but added there were further challenges in other areas as well.