The EU's chief Brexit negotiator has said the EU is working to improve its backstop text and insisted it would respect the territorial integrity and constitutional order of the United Kingdom.
Michel Barnier said the EU was not seeking a border along the Irish Sea as a result of the backstop.
Speaking following a meeting of EU European and Foreign Affairs ministers in Brussels, Mr Barnier said: "We are ready to improve this proposal. Work on the EU side is ongoing.
"We are clarifying which goods arriving in Northern Ireland from the rest of the UK would need to be checked and where, when and by whom these checks could be performed.
"We can clarify that most checks can take place away from the border, at a company premises or in the market [place].
"We need to de-dramatise the checks that are needed. These checks are caused by the UK's decisions to leave the EU single market and the customs union.
"What we're talking about is not a border, not a land border, not a sea border. It's a set of technical checks and controls, just about all of which cannot be put other than in a physical place in Northern Ireland.
"So I hope that on the basis of simple, practical, objective provisions we'll be able to find a position whereby this improved backstop can be acceptable.
"It will not in any case take the form of a border because we respect the territorial integrity of the UK, and we respect the constitutional order of the UK."
Both Mr Barnier, and Tánaiste Simon Coveney, with whom he held talks for an hour earlier, stressed that agreement - or at least substantial progress on the backstop - needed to be reached in October at the summit of EU leaders, and not November, when an emergency summit is expected to be called.
Mr Barnier called October the "moment of truth".
Mr Coveney said all sides in the Brexit dispute should try to reach agreement on the Irish backstop by the October European Council.
He said there was a "real appetite" in the Task Force for intensification of talks with London and for that to happen sooner than later.
Mr Coveney said that both the Task Force and Ireland agreed that negotiations should not drift into November and potentially December.
"We want to be in a position where EU leaders are making decisions in October," he told reporters in Brussels.
He called on the UK to intensify its engagement in negotiating the detail of the backstop, adding that the UK should be negotiating in Brussels, rather than trying to lobby member states separately in various capitals.
"Everybody wants a deal here. Everybody loses without a deal."
Mr Coveney said there was the basis of an agreement and that Mr Barnier and the task force had "looked at every possible angle".
"We need a withdrawal agreement that stands up to scrutiny, and can be legally challenged and successfully defended.
"This isn't a political agreement whereby constructive ambiguity can help get things across the line.
"It's a legal text."
Mr Coveney said the EU was showing flexibility, but that the UK needed to come forward with a new text on the backstop since it had rejected the EU's initial draft.