Pollster Red C said its latest national survey – weeks after the Brexit result – shows a sharp rise in support for reunification since a similar opinion poll six years ago.
Asked how they would vote if a referendum was held tomorrow, 65 per cent of the sample electorate said they would vote in favour of a united Ireland.
Some 30 per cent said they would vote against it, while five per cent said they were undecided.
The findings show an eight per cent jump in support for a united Ireland since Red C posed the same question in a poll carried out for the Sunday Times in 2010.
The shock Brexit result last month has sparked a renewed debate about a potential referendum on the Irish border. A majority of voters in Northern Ireland want to remain as part of the European Union.
Remain campaigners, including Sinn Fein Deputy First Minister Martin McGuinness, have insisted their wishes must be respected.
But Leave backers, among them Democratic Unionist First Minister Arlene Foster, have insisted the EU referendum result is a UK-wide decision.
The leader of the Republic’s main Opposition party Fianna Fail, Micheal Martin, said he hoped the Brexit result would lead to a united Ireland.
However, Taoiseach Enda Kenny has in recent days retreated from his earlier talk of a border referendum.
The latest Red C poll also shows Mr Martin’s Fianna Fail is the most popular party in the republic.
Arch-rivals Fine Gael rely on his support for their minority government, formed after weeks of negotiations following a huge split in the vote earlier this year.
In a cross border survey last year by broadcasters RTE and BBC Northern Ireland, 66 per cent of people in the Irish Republic said they would like to see a united Ireland in their lifetime.
But only 30% in Northern Ireland held the same view, with 43 per cent saying they would not like to see reunification.
For the latest poll, carried out for bookmaker Paddy Power, Red C interviewed a sample of 1,000 voters in the Irish Republic between July 25 and 27.
Support for a united Ireland was equal at 65 per cent among both men and women.
More (69 per cent) in less well-off social groups than better-off groups (59 per cent) said they would vote for reunification.
Voters living in Dublin (56 per cent) were less likely to vote in favour of a united Ireland than those living outside the capital (68 per cent to 69 per cent).
Sinn Fein (79 per cent) and Fianna Fail (71 per cent) supporters were most likely to back reunification, while Fine Gael (58 per cent) voters were least likely.