Sinn Féin's health spokesperson Louise O'Reilly has said she believes another election is a real possibility.
However, she stated that all avenues to forming a government must be explored.
Both Fianna Fáil and Fine Gael have reiterated their intention not to go into a coalition with Sinn Féin which makes forming a government more difficult.
Ms O'Reilly, who is on her party's negotiating team for government formation talks, believes that another poll could produce a similar result.
Speaking on Newstalk Breakfast today, she said "not a huge amount of progress" was made during a phone call between her party leader Mary Lou McDonald and Fianna Fáil leader Micheál Martin yesterday.
However, she said the party leaders will be meeting next week to hold further discussions.
She said: "What I would be interested to know from Micheál, and indeed some people in Fianna Fáil, is if they believe the change that people looked for, that they voted for, would be possible in a Fianna Fáil/Fine Gael arrangement.
"Let's not forget, Micheál Martin ruled out categorically doing business not only with Sinn Féin but also with Fine Gael.
"In the cold light of day post-election when the numbers are counted up, what we're saying is our democratic mandate is a valid as anybody else's and we believe we should be included because people are looking for change."
She added: "For our part, we certainly remain open to discussions.
"I don't think now is the time to be doubling down on red lines that were issued by Fianna Fáil before the election.
"What we're saying is there is an alternative, there's a progressive alternative...we're saying don't close off alternative options."
Democratic credentials
Ms O'Reilly said the election result solidified Sinn Féin's credentials as a party for change.
She said: "I don't think there can be any doubt about over our democratic credentials given the result we got in this election and backing that we got and the fact we won the popular vote.
"We increased our vote share and came away with the largest number of votes of any party which quite an achievement."
Ms O'Reilly said that her preference for the 33rd Dáil would be to negotiate "a republican programme for government that delivers for people".
However, she believes that another election in the coming weeks "is a very real possibility".
She said: "What I would say though is we've just had an election and the likelihood after another election is that the result wouldn't be hugely different.
"I think it behoves everybody to try their best to put together a government based on the result we have just received."
