Labour Party leader Eamon Gilmore has said the latest Sunday Business Post/Red C poll is very encouraging for his party and it signalled a three-way political contest was now emerging.
People, he said, were looking for an alternative to Fianna Fáil and Fine Gael.
Mr Gilmore said the poll may indicate that the political map is now being recast.
Adding that he did not want to make exaggerated claims for what is happening, he said the challenge for Labour was to convert the good poll results into real results in an election.
To achieve that Labour will continue with organising in new areas, selecting more candidates and bringing its message to the public.
He added there was now an ‘unanswerable case’ for RTÉ to accept the public should be offered a three-way debate by the leaders of the three main parties.
Minister for State Dick Roche has said that there is resilience within Fianna Fáil following today's poll.
He told RTÉ's The Week in Politics programme that the Government has had to take difficult decisions to cut public spending, but he believes there is more resilience among Fianna Fáil backbenchers than they are given credit for.
Mr Roche said he believes these backbenchers will continue to back the Government and the Taoiseach for the next two years.
Fine Gael's Charlie Flanagan said that over the last 15 months all opinion polls have shown that Fine Gael is the biggest party.
He said the Government has no plan, and is displaying neither interest nor enthusiasm in dealing with the country's problems.
FF could have done worse in poll - O'Keeffe
Minister for Enterprise, Trade and Innovation Batt O'Keeffe has said Fianna Fáil could have done worse in the latest opinion poll.
The Red C poll revealed that Labour support was up seven points to 24%, while Fianna Fáil was down one point to 23%.
Speaking on RTÉ Radio’s This Week, Mr O'Keeffe said Labour had benefited from its recent party conference and from the controversy over TDs' and Senators' pensions.
The Minister said there was no need for the Government to put pressure on politicians who had not given up their pension entitlements, and it was up to each of them to decide what they should do with the income.
Red C questioned 1,000 voters around the country on Monday, Tuesday and Wednesday, at the height of the controversy over ministerial pensions, and after all the parties - with the exception of Fianna Fáil - had held their annual conferences.
The poll found Fianna Fáil support down one point to 23%, leaving the party in third place just days before the second anniversary of Brian Cowen's election as Taoiseach.
Labour are now in second place, which is the first time it has ever achieved that position in a Red C poll.
Fine Gael is down two points to 33%, but maintain a commanding lead as most popular party.
The Green Party is up one point to 6%, while Sinn Féin dropped four points to 6% support.
Independents and others are down one to 8%