Sinn Féin has continued to build on its February election success, recording the party's highest-ever Red C poll rating.
The poll showed Mary Lou McDonald's party on 30% while Fine Gael continue in front on 33% — down from 37% after weeks of social media campaigning against Sinn Féin.
However, the Sinn Féin leader says "nobody will get carried away" by the poll result.
"There is much work to be done," she said. "But it does underline the reality that people want change, and this Government won't deliver it.
"Covid-19 has impacted people's lives in ways none of us could have envisaged, but this has not dampened the appetite for a fairer society. It has, in fact, reaffirmed it.
"The pandemic has exposed the fault lines and highlighted the great inequalities and vulnerabilities faced by many.
Meanwhile, Fianna Fáil TDs are concerned about a snap election next year after polling at just 12% in the Business Post/Red C poll. There are also fears of a perceived "loss of identity" in the coalition.
Despite the message from leadership to dismiss polls, numerous Fianna Fáil TDs at various stages of their political careers have told thethat they are concerned.
One TD said there is "real concern about an election next year, we have an unstable three-party Government — anything could happen. People are worried about the existence of Fianna Fáil after the next election".
"If we perform as we have in the polls, we'll only get 14 seats or so, no Fianna Fáil TD would be elected in Dublin," the TD said.
Polls have been a consistent concern for some within Fianna Fáil and despite recent controversies in Government stemming from Fine Gael, it appears Micheál Martin's short tenure as Taoiseach has not swung more support in their favour.
Housing minister Darragh O'Brien rejected the idea that his party is being "squeezed".
"I never put much store in polls, whether we up or down within them, and I think there is a long history of Fianna Fáil being underestimated in polls," he said on RTÉ.