DUBLIN - Ireland is exploring the idea of checking live animals and animal products from Britain as they arrive at ports on the whole island of Ireland if there is a no-deal Brexit, Prime Minister Leo Varadkar said on Friday.

How to manage the land border between European Union member Ireland and British-run Northern Ireland remains the most contentious part of a proposed agreement on the terms of Britain's departure from the EU. Both contenders to become the next British prime minister want that agreement renegotiated.

Dublin repeated this week that it would not impose any restrictions along the now-open border if Britain quits without a transition agreement. But the Irish said for the first time they would need to make checks somewhere to protect the EU single market.

"The kind of things that we're looking at and proposing, for example, is that the entire island of Ireland will be treated the same when it comes to agriculture or food and that any SPS (sanitary and phytosanitary) checks would happen at the ports," Varadkar said in an interview with Ireland's Newstalk radio station.

"That would mean Britain accepting that Northern Ireland is being treated differently. The other things obviously are checks at business level and random checks and controls, and we'll have to have a lot more of them anyway because of smuggling."

Ireland is in talks with the European Commission over how it could make the necessary checks without re-imposing controls on the 500-km frontier, which was controlled by military checkpoints controlled the border until a 1998 peace deal ended three decades of sectarian violence in the province.

Any checks between Britain and Northern Ireland would be anathema to the Democratic Unionist Party (DUP), the small pro-British party that props up the minority government in London. The DUP has been part of the opposition that rejected the proposed agreement three times in the British parliament.

"This is not a good solution, this is vastly inferior to what we negotiated with Prime Minister (Theresa )May and is vastly inferior to the North's current model," Varadkar said

The impact of a no-deal Brexit on Northern Ireland would be harder than on any other part of Europe, Varadkar warned, and the so-called backstop in the proposed Brexit agreement remained the best compromise.

The backstop was negotiated by May's government with the EU. In effect, it would have kept Northern Ireland and the rest of Britain in a customs union with the EU.

The backlash in Britain's parliament to the agreement led to its rejection. That in turn led to May's being forced out as leader of the Conservative Party and will ultimately result in her being replaced as Prime Minister.

Varadkar said the next British prime minister will face a "very serious reality check" on Brexit upon taking office. And he rejected as "incorrect" a claim by the leading candidate, Boris Johnson, that the border issue could be resolved in a transition phase.

(Reporting by Padraic Halpin; editing by Andrew Heavens, Larry King) ((padraic.halpin@thomsonreuters.com; +353 1 500 1504; Reuters Messaging: padraic.halpin.thomsonreuters.com@reuters.net))