DUBLIN -- Ireland's governing coalition parties privately expressed relief Sunday as an opinion poll showed an unexpectedly large majority saying they will endorse the new European Union budget-discipline treaty in a public referendum May 31, easing concerns Irish voters might favor those urging its rejection.

The "yes" side had feared the French and Greek elections of May 6 had boosted those in Ireland urging voters to kick back at the austerity entailed by the country's EU and International Monetary Fund bailout and to reject the new fiscal treaty in the public vote.

Coalition party spokesmen said they were relieved by the poll's findings.

Ireland is the only one of the 25 countries participating in the fiscal union--the U.K. and the Czech Republic are staying on the sidelines--whose constitution requires the public passing of the treaty in a referendum. An Irish rejection wouldn't stall the new fiscal union, but would add to the growing chorus of European electorates questioning whether austerity provides a solution to the region's debt crisis.

The Red C poll for The Sunday Business Post newspaper, however, found that Irish voters will approve the EU fiscal treaty by a majority of 63% to 37% when those who say they are undecided are excluded.

That majority is higher than the 58%-to-42% lead for the "yes" side in a poll the newspaper published two weeks ago--before the formal start of the month-long campaign--and suggests that the "yes" side has built a strong lead.

Also, the latest newspaper poll said that when the undecideds are included, 53% said they will vote "yes" and 31% said they will vote "no," with 16% saying they are undecided, suggesting that the "yes" side's lead is "commanding" and that the "no" side needs a dramatic change to prevent the treaty being passed, with just two and a half weeks to go to polling.

Ireland's deputy leader, Eamon Gilmore, in the coalition led by Prime Minister Enda Kenny, sought to build on the poll advantage. In a televised debate Sunday, Gilmore accused the "no" side of asking the Irish "to take a punt" by risking future funding for the country.

The government appeared to have had a difficult early-stage campaign, Communications Minister Pat Rabbitte had said ahead of the poll, because, he believed, the "no" side had "misrepresented" the pledge of French President-elect Francois Hollande to re-engineer the compact.

Kenny's coalition has warned that rejection will cut Ireland off from accessing new bailout funds from the permanent European Stability Mechanism--if it were ever to need such funds in the future--and harm the country's fragile economic recovery. Ireland aims to get back to full market funding before the end of next year, when the EU and IMF loans expire.

The leading proponent of the "no" side, the opposition party Sinn Fein, led by Gerry Adams, has dubbed it the "austerity treaty" because it sets stricter oversight on governments to control budget deficits.

"It's a charter for cuts," Adams said in the televised debate.

The latest poll also had good news for Sinn Fein, showing it increased its support to 21% of voters, its highest ever in a Red C poll, the newspaper said.

Fianna Fail, the largest opposition party but a supporter of the treaty, has the support of 19% of voters, up two percentage points, according to the poll.

Support for Fine Gael, the bigger governing party led by Kenny, is at 29%, down three percentage points from the previous Red C poll, while Gilmore's Labour, the junior coalition party, has the support of 13% of voters, down one percentage point from the previous poll.

-By Eamon Quinn, Dow Jones Newswires; +353 1 6762189; eamon.quinn@dowjones.com