At an EU summit in Sweden, Prime Minister Theresa May's government was urged to clarify how much Britain will pay in settlement of its financial accounts with the bloc and to ensure that there is no hard border created between Ireland and Northern Ireland.
Britain is due to leave the EU on March 29, 2019, but it must complete the complex and unprecedented departure process by next October so that parliaments can ratify any agreement.
"Great Britain need to clarify what they mean with the financial responsibility," the summit host, Swedish Prime Minister Stefan Lofven, told reporters in the city of Goteborg.
"We all hope that we can decide on the next phase but we still have some way to go," he said.
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Britain has suggested that it might be willing to pay USD 23 billion to fulfil its financial commitments, while EU officials have said the figure would more likely be between USD 71-118 billion.
"We've been given assurances . that there will be no hard border in Ireland, that there won't be any physical infrastructure, that we won't go back to the borders of the past," Varadkar said. "We want that written down in practical terms in the conclusions of phase one."
"It's 18 months since the (Brexit) referendum. It's 10 years since people who wanted a referendum started agitating for one. Sometimes it doesn't seem like they've thought all this through," he said, of May's government.
"Of course we want to move forward together, talking about the trade issues and trade partnership for the future," she said.
"I look forward to the European Union responding positively to that so we can move forward together and ensure that we can get the best possible arrangements for the future."
This EU summit in Sweden is ostensibly about employment and social welfare, but May has been using her visit to hold bilateral talks on Brexit with several leaders, including Lofven, Varadkar and EU Council President Donald Tusk.
"The clock is ticking," European Commission President Jean-Claude Juncker said today. "I hope that we will be able to come to an agreement as far as the divorce is concerned in the December (EU) council but work has still to be done.