The British Prime Minister has ruled out any delay to the Brexit process as she told European Union leaders that her "Chequers" plan was the only credible route to a deal.
Theresa May set out a blueprint to her 27 counterparts over dinner in Salzburg after being told by EU chiefs that significant elements of it would have to be reworked.
Brexit, internal security and migration were discussed at the informal summit of EU leaders.
It is the first time leaders have had an encounter with Mrs May since the "Chequers" paper was published in July.
However, at the gathering in Austria, the British Prime Minister told them there would be no delay beyond the UK's March 2019 departure, no second referendum and therefore the onus was on the EU leaders to find a solution if they wanted to avoid a no-deal Brexit.
European Council president Donald Tusk said Mrs May's Brexit blueprint was a "welcome evolution" in the UK's approach but major issues remained to be resolved, including avoiding a hard border on the island of Ireland and the future trading relationship between Britain and the EU.
Warning that there was "less and less time" to reach a deal before the UK's 29 March 2019 exit date, Mr Tusk confirmed he would propose an emergency EU Brexit summit in November.
Arriving at the meeting in Salzburg, Mrs May said her "Chequers" plan was "the only credible and negotiable plan on the table that delivers no hard border in Northern Ireland and also delivers on the vote of the British people".
She added: "If we are going to achieve a successful conclusion then, just as the UK has evolved its position, the EU will need to evolve its position too."
Her comments came just hours after Mr Tusk said that on key issues "the UK's proposals will need to be reworked and further negotiated".
Following the dinner, the leaders of the Lithuania and Slovakia said that there has been no progress on Brexit and the Irish border.
"At this stage, it's a standstill. There is no progress," Lithuanian President Dalia Grybauskaite told Reuters.
Slovak Prime Minister Peter Pellegrini added: "On the border issue, there has been no progress. We'll see what the 27 discussion will show tomorrow."
Taoiseach Leo Varadkar has delivered a downbeat assessment of the Brexit negotiations.
He dismissed suggestions there had been progress in recent weeks on the Irish backstop, and said that the UK still had to present an alternative text to the EU's initial draft which was rejected by Mrs May last March.
EU to suggest simplifying checks post-Brexit
Meanwhile, RTÉ News understands that the EU will suggest that checks would need to be carried at British and Northern Irish ports on only one category of goods moving from Great Britain to Northern Ireland in the event of the backstop taking effect.
The EU’s chief Brexit negotiator Michel Barnier has told member states that checks could be simplified across the board.
In all, four categories of goods would be affected if the Irish backstop took effect, and Northern Ireland was to remain in the EU customs union and single market.
Mr Barnier said that only live animals, animal-derived goods and food products would need to undergo physical checks at the actual ports in Great Britain and then in Northern Ireland.
Briefing EU European and Foreign Affairs ministers in Brussels last night, Mr Barnier said that these checks already take place on such products or goods that move between the rest of the UK and Northern Ireland.
This more detailed breakdown of what the EU regards as necessary checks will form the bulk of what Mr Barnier last night termed an "improved" text on the Irish Protocol, RTÉ News understands.
Mr Barnier told ministers that the protocol would have to respect the constitutional integrity of the United Kingdom, and that those were the "constraints".
British officials have already described such changes as unacceptable. London's position remains that the backstop must be UK-wide for customs, in order to avoid customs checks along the Irish Sea.
According to a briefing note seen by RTÉ News, and confirmed by a second source, Mr Barnier broke down the checks that would be required under the backstop into four categories, only one of which – animal and food products - would require checks at ports.
The first category was customs, which is seen as the most sensitive.
According to the note, customs declarations could be filled in in advance. The only physical check would be the scanning of a barcode on a container.
Once the scans had been done there would be a risk analysis of the physical need for actual checks of the goods within the container.
Mr Barnier told ministers that such checks were already common in the EU’s Union Customs Code and he cited the fact that customs authorities deployed such technology on goods moving between Spain and the Canary Islands, and vice versa.
The second type of control would be for VAT and excise duty.
Mr Barnier said that the information contained within the customs declaration "would suffice" to calculate the final payment.
The third kind of checks would relate to conformity with EU standards and regulations for industrial goods.
These, he said, could be done by what he termed "market supervisory authorities" at the point of sale, and on the basis of the customs declaration already filled in.
The fourth category of checks, under EU sanitary and phytosanitary (SPS) rules, would, however, be required at British and Northern Irish ports.
According to a senior EU official, Mr Barnier explained that such checks already exist on live animals moving across the Irish Sea, but that at present only 10% of consignments are checked.
"This would have to increase substantially," the official told RTÉ News.
Mr Barnier also told EU ministers that the new set of checks and controls would only be required on between 40% and 45% of the trade moving between Great Britain and Northern Ireland.
That is because, according to the chief negotiator, the remaining percentage moves through Dublin.
In a post-Brexit scenario these goods would be subject to checks anyway.
Mr Barnier also told ministers that the backstop was a "safeguard solution" that could be replaced by "new elements" as part of the future relationship.
He said that if the UK wished to remain in the customs union then the EU could "go even further".
The EU’s chief negotiator said there was a need to "protect the UK’s territorial integrity" and that those were the constraints governing the backstop.
According to a separate source who was present at the meeting: "He went through what the backstop means. The [animal health and food safety] SPS checks. They’re not in principle different from what already goes on. They would just be increased, but then could be reduced if we do other agreements on them.
"The main issue is customs, which is mostly paperwork, but it doesn’t need to be done on the [sea] border. It can be done when you load or offload."
It is understood Mr Barnier said there were key points of "convergence" between Theresa May’s Chequers White Paper.
According to one official present: "He said Chequers was valuable, and there were many points of convergence between the Chequers White Paper and our position.
"We never understood the White Paper as, here are 99 pages, please sign on the dotted line and we have an agreement. We always took it, and it was explained to us publicly, as a sign of movement and a sign of ambition and it was a position paper that was supposed to be discussed."
Additional reporting Tony Connelly