But it is likely the main focus of the meeting of the world's seven wealthiest industrial nations will be dominated by discussions around the USA president's controversial trade strategy.
The EU backstop option has been rightly criticised for reducing the single market "access of Northern Ireland to ... goods, including agricultural and electricity".
The EU proposed keeping Northern Ireland in the customs union but this was rejected by the government as well as Northern Irish party the DUP, which is holding together Mrs May's minority government. "Time is running out", Barnier said.
Ireland's ideal scenario would be for Britain to stay in the EU's customs union and single market, ensuring regulation is not a barrier to intra-EU trade.
The Best for Britain called on the country's Prime Minister Theresa May to present her clear proposals in autumn on the country's future after the withdrawal, as it was unacceptable "to hold the country hostage" of internal governmental divisions.
This will see the UK retain parts of the EU's customs union in the event of a wider UK-EU agreement finding no solution to the issue; but Brexiteers had become concerned as to whether the proposal would truly be "time-limited", as promised.
But he said: "It is now essential that government makes progress on our long-term customs and other border arrangements".
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"Is it a workable solution to avoid a hard border?" Potential barriers to worldwide trade were thrown up by the Government's decision to leave the Customs Union and the Single Market, he claimed.
Mr Barnier said that "much remains to be done" on the withdrawal issues of data protection, geographical indications for food and drink and the resolution of proceedings relating to the United Kingdom which are ongoing at the end of the transition period.
Britain now expects the future arrangement to be in place by the end of December 2021 at the latest, a year after the end of the post-Brexit transition period.
One of the key questions raised by Barnier relates to whether the backstop has a time limit on it.
The UK signed up to a backstop in December following pressure from Ireland and the European Union, but has failed to put forward any alternatives since then, leaving it as the only agreed option in the run up to a crucial summit at the end of June.
Who supports it? This is the official policy of the Liberal Democrats and the favoured outcome of the Best for Britain pressure group and the People's Vote campaign for a second referendum on the final Brexit deal.
The European Commission stands ready to aid countries hit by Britain's departure from the European Union and other external shocks, Budget Commissioner Guenther Oettinger said on Friday.