BELFAST (Reuters) - Irish Prime Minister Leo Varadkar called on Friday for the European Union and Britain to find “unique solutions” to their Brexit logjam, including a bespoke customs union.

That would solve the problem of a hard border in Ireland once Britain has left the EU, something that is of great concern to Dublin.

Varadkar, a new face at EU summits since taking office in June, also suggested Brussels may accede to Britain’s insistence that a post-Brexit body other than the European Court of Justice oversee bilateral issues, such as citizens rights and aviation regulation.

He said, however, that all these “practical solutions” would need to be asked for and would not be offered.

Varadkar was speaking in the British province of Northern Ireland as part of a drive to find a compromise that would avoid a hugely damaging hard border being erected across the island of Ireland.

Dublin is hoping compromise can be reached ahead of a key Brexit summit in October, which Varadkar described as a “historic meeting for this island.”

“Time is running out and I fear there will be no extra time allowed,” he told students at the Great Hall at Queen’s University in Belfast.

In a wide-ranging speech during his first visit to Northern Ireland as Irish prime minister, Varadkar made several proposals to try to break the Brexit logjam.

He said a bilateral customs union could be based on one the EU currently has with Turkey. “If we have one with Turkey. Surely we can have one with the United Kingdom?” he said.

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British Prime Minister Theresa May has said Britain will leave the EU’s customs union when it leaves the bloc in order to pursue its own trade agreements with countries around the world.

A bilateral customs union would appear to imply that both sides would be free to strike deals with third parties, though Varadkar did not provide detail of the proposal.

British membership of the European Free Trade Agreement was also an option, or failing that, Britain could remain in the single market and the customs union during a transition phase, he said.

Asked about the proposals, a spokeswoman for the British government said Britain had “been clear that we want a deep and special future partnership with the EU, including a bold and ambitious free trade agreement and a customs agreement.”

IRISH BORDER?

Ireland, which after Brexit will have the EU’s only land border with the United Kingdom, is widely seen as the EU country most exposed to the fall-out from Britain’s leaving.

The issue of how the Republic and Northern Ireland will fare is particularly sensitive given the decades of violence in the province over whether it should be part of Britain or Ireland. Around 3,600 people were killed before the 1998 peace agreement.

Varadkar last week said his government would oppose any customs posts or immigration checks on the land border between the Republic of Ireland and Northern Ireland, but he did not say where they should be placed instead.

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There have been no customs or immigration checks on the 500 km (310 mile) border since the European single market came into effect in 1993. About 30,000 people cross every day without any border checks.

The future of that border is one of three issues -- along with EU citizens’ rights and British budget payments to the EU -- on which Brussels says there must be “significant progress” before talks can begin on the free-trade deal London wants.

Varadkar also suggested that the EU may be considering compromise on its insistence that the European Court of Justice (ECJ) oversee key elements of any future relationship, such as citizens’ rights to live in the United Kingdom and the oversight of regulation of sectors like aviation and nuclear power.

May’s opposition to any oversight by the ECJ has been a key stumbling block in talks.

“At the moment the mechanism by which most European agreements are upheld is through the European Court of Justice and the United Kingdom has indicated it no longer wishes to be part of. So we would need to develop some other mechanism,” Varadkar said.