* UK needs border deal to secure EU transition deal
* EU says if no deal by Monday, delay to 2018
* "So be it" if December deadline missed, Dublin warns
* N.Ireland's DUP threatens to withdraw support for PM May (Adds DUP warns may withdraw support for British government)
DUBLIN/BRUSSELS, Nov 30 (Reuters) - Ireland needs Britain to provide "significantly more clarity" on its plans for the Irish border, Foreign Minister Simon Coveney said on Thursday, denting hopes that London was on the verge of a deal to move on to the second phase of Brexit talks.
But British Prime Minister Theresa May's room to offer additional concessions to Dublin appeared extremely limited as the Northern Ireland party propping up her government hinted it might withdraw its support if she gives too much.
Avoiding a so-called "hard border" on the island of Ireland is the last major hurdle before Brexit talks can move to negotiations on Britain's future trade relationship with the EU and a possible two-year Brexit transition deal.
A mis-step by May could bring down the British government or spook British businesses fearful of a cliff-edge Brexit without a transition deal.
"We are looking for significantly more clarity than we currently have from the British negotiating team," Coveney told parliament in Dublin, adding that "constructive ambiguity" from Britain would not suffice.
"Hopefully we will make progress that will allow us to move on to Phase 2 in the middle of December," he said. "If it is not possible to do that, so be it."
Britain in the coming days needs to demonstrate "sufficient progress" on three key EU conditions -- a financial settlement, rights of expatriate citizens and the Irish border -- for leaders to give a green light to trade talks at a summit on Dec. 14-15.
With significant progress on the financial settlement and citizen rights, a deal on the Irish border would pave the way for Brussels to offer British Prime Minister Theresa May a transition deal as early as January.
Britain's Times newspaper, without citing a source, said London was close to a deal after a proposal to devolve more powers to the government of its province of Northern Ireland so that it could ensure regulations there did not diverge from the EU rules in place south of the border across the island.
The border between EU-member Ireland and the British region of Northern Ireland will be the UK's only land frontier with the bloc after Brexit, and Dublin fears a hard border could disrupt 20 years of delicate peace in Northern Ireland.
Ireland has called on Britain to provide details of how it will ensure there is no "regulatory divergence" after Brexit in March 2019 that would require physical border infrastructure.
But any attempt at a solution will have to convince Northern Ireland's pro-Brexit Democratic Unionist Party, whose 10 members of parliament are propping up May's government.
The party ratcheted up the pressure on Thursday by suggesting it might withdraw its support for May's government.
"If there is any hint that in order to placate Dublin and the EU they're prepared to have Northern Ireland treated differently to the rest of the United Kingdom, then they can't rely on our vote," DUP member of parliament Sammy Wilson said in an interview with the BBC.
European Council President Donald Tusk, who last week set an "absolute deadline" of Monday for May to demonstrate sufficient progress on the three issues, is due to fly to Dublin on Friday for talks with Irish Prime Minister Leo Varadkar in a bid to break the deadlock.
May will then hold talks in Brussels on Monday with EU chief executive Jean-Claude Juncker and his chief Brexit negotiator, Michel Barnier, and will hope to secure a green light to trade talks at a summit on Dec. 14-15.
Barnier said on Wednesday the summit would be able to discuss a transition period and that the EU would define a "framework" next year of the "new partnership" with Britain that would follow the transition.
May has insisted she wants any new offers to be met with simultaneous assurances from the EU that it will maintain the open trading relationship which businesses are demanding to know soon if they are to maintain investment levels in Britain. (Editing by Padraic Halpin and Catherine Evans)