The contest to lead the next Government could be between Fine Gael and Sinn Féin, Minister for Transport Leo Varadkar has suggested.

Mr Varadkar said he could see the potential for a scenario where the electoral contest at the next general election could be “Fine Gael versus Sinn Féin to lead the next Government”. But he adamantly ruled out any coalition between the two parties because they were ideologically and politically too far apart.

Asked when he could see his party in Government with Sinn Féin, Mr Varadkar said “I don’t”. He said there was too much between them, “too big a gap between us on policy” and outlook, to be bridged.

The Minister was speaking to reporters at the Golden Shears World sheep shearing and wool handling championship in Gorey, Co Wexford.

He and Cabinet colleague Minister for Agriculture Simon Coveney attended the opening day of the championship where they walked through the exhibition stands with Fine Gael EU candidate Simon Harris and posed for photos, along with Government chief Whip and Wexford TD Paul Kehoe, Wicklow TD Andrew Doyle and Wexford Senator Michael D’Arcy.

In the big tent where the sheep shearing heats were taking place the expectation was that one of the Ministers would shear a sheep but it was ruled out on health and safety grounds that they could injure an animal.

Asked about the high showing of Sinn Féin in the polls, Mr Varadkar said it was not surprising because they were acting like a classic opposition party. He said they were making political promises to “abolish the universal social charge, water charges and the property tax”.

He said “they are telling people what they want to hear but it’s not very honest”.

He said a Castleknock constituent had criticised him for the party breaking its promises in Government, but she was then going to vote for a party making outrageous promises.

It was a mid-term election for his party and the first in a very long time for Fine Gael in Government. He said the campaign was not as difficult as they expected. Unemployment was less of an issue than it had been. “It hasn’t gone away” but it was not as big an issue because of what the Government had been doing for the past three years and the situation had improved.

Earlier, asked about the rise of far right parties and candidates in the European elections Mr Coveney said he hoped there wasn’t a lot of talk in that direction in Ireland. “That’s not the direction we need to go in.”

The Minister pointed out that Irish people emigrated to “the US, Canada, Australia, Britain obviously” and it had been good for the emigrants and for those countries. He said immigration was also a part of Irish life and had been good for Ireland.

He described the Ireland South constituency where Wicklow TD Mr Harris is standing as “huge with four Leinster counties and the entire of Munster”, but he said they had three really good candidates.

Mr Harris said the electorate were concerned about local issues but he said the problems they raised at local level were linked to solutions in Europe such as the €70 billion research and development fund and the youth guarantee on employment for the under 25s.

The candidate said he had kissed just one baby on the campaign, 10-weeks old Emma, daughter of Government chief whip Paul Kehoe, but he had shaken thousands of hands. He estimated that it was about 250 handshakes “at a march” on a canvass.

He said the important thing when a campaign moved so fast was making contact, “grab a shoulder, shake a hand, kiss a baby”.