The embattled British premier was set to meet EU President Donald Tusk on the sidelines of a summit with ex- Soviet states in Brussels in a bid to unlock negotiations on a future trade deal.
Impatient EU leaders were increasingly hopeful she would bring a new proposal on the thorny issue of Britain's exit bill, after senior British ministers agreed earlier this week to improve the offer to a reported 40 billion euros (USD 47 billion).
"These negotiations are continuing but what I'm clear about is that we must step forward together. This is for both the UK and the European Union to move to the next stage," she told reporters.
At a meeting in Gothenburg, Sweden a week ago, Tusk gave May until the start of December to make "much more progress" in order to unlock trade negotiations at an EU summit on December 14-15.
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May will also meet her counterparts from Lithuania and Denmark.
The EU insists Britain must tie up divorce terms -- the bill, the Irish border and the rights of EU nationals living in Britain -- before there can be any talks on future relations.
European Commission President Jean-Claude Juncker said he was more confident than before about a deal but said nothing would be decided before he had dinner with May on December 4.
EU member states have become increasingly impatient for Britain to comply, and increasingly worried that May's fragile Conservative government is unable to do so even if it wanted to.
"It's high time the English came with clear proposals," a European diplomatic source said on condition of anonymity. "The more the English let us stew, the more unified we become."
But Ireland remains a major sticking point, with Dublin stepping up threats to veto a deal if its concerns about the border with British-ruled Northern Ireland are not taken into account.
Coveney admitted however that a political crisis in Ireland over the deputy premier's handling of a police whistleblower case had left the government in a "precarious position".
"The financial question is the least difficult issue in the negotiations. So far, the Irish question is unsolvable," an EU diplomat said.
Britain is reportedly set to double its offer to settle its commitments to the EU budget from 20 billion to 40 billion, but the EU has so far said the true figure should be closer to 60 billion.
May meanwhile said her presence at the so-called Eastern Partnership Summit with six former Soviet states showed that Britain was "unconditionally committed to maintaining Europe's security" despite Brexit.
The British premier also took aim at Moscow, saying Europe must be "open-eyed to the actions of hostile states like Russia which... attempt to tear our collective strength apart.
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