Newly-elected Fine Gael TD Neale Richmond has said his party will "probably" be in opposition in the next government.
The former Senator was elected in the Dublin Rathdown constituency, along with this party colleague Josepha Madigan.
They share the constituency with deputy Green Party leader Catherine Martin, who took the third seat.
Deputy Richmond told Newstalk Breakfast: "If others want to form a government, then we do have to play a pro-active role".
But he added: "We wouldn't be going into government with Sinn Féin, that's not our prerogative".
Asked about ignoring the Sinn Féin surge, he said: "It is about responsible government - and a lot of people have heard over the last two days have heard talk about mandates and respecting democracy.
"We sought a mandate by saying quite clearly that we wouldn't go into government with Sinn Féin.
"We have to be respectful to the people who voted for Fine Gael candidates up and down around the country - that won't be changing".
Asked what the next step for his party could be, he said: "At this stage I have to be honest - I'd say we probably would be in opposition.
"But it's a long day and indeed possibly days ahead".
But he suggested that "despite the rhetoric of Micheál Martin before the campaign, I think there's a lot of people in Fianna Fáil who are eager" to see a Fianna Fáil/Sinn Féin government.