"Our red line also respects and protects Northern Ireland's constitutional place in the United Kingdom", she added.
Avramopoulos also said the bloc's no-deal contingency plans on security were driven by "goodwill", stressing the bloc would want to continue cooperating with Britain closely, including on sharing intelligence.
'Of course the Government are going to whip this vote extremely hard, but what I would say is that the whips would be doing incredibly well if they were to halve the numbers.
European Union's chief Brexit negotiator, Michel Barnier attends a media briefing with Britain's Secretary of State for Exiting the European Union, Dominic Raab, after a meeting at the EU Commission headquarters in Brussels, Belgium on August 21, 2018.
The former Brexit minister, now a senior figure in the fight against the Prime Minister with the hardline European Research Group, previously said 80 Conservatives would be prepared to oppose the Prime Minister if her deal with the EU kept Britain too closely aligned to it.
Mrs May, meanwhile, urged MPs across the Commons to act in the national interest and back a Brexit deal amid warnings that "decisive" progress is needed in the negotiations before a crunch Brussels summit next week.
"If we stay on our current trajectory we will go into the next election with the government having delivered none of the benefits of Brexit, with the country reduced to being a rule-taker from Brussels and having failed to deliver a number of manifesto promises and on the Lancaster House speech", he writes.
UK Prime Minister Theresa May was challenged by a number of her cabinet ministers, including Liam Fox, the global trade secretary and Michael Gove, the environment secretary, on Thursday who voiced concerns over her new backstop plan, fearing it would keep the UK in a customs union with the EU for an open-ended period of time.
20 dead after crash involving wedding limo in NY
Patrick Cushing, who worked for the New York State Senate, and his girlfriend, Amanda Halse, also died in the crash. Abeling said in an interview from upstate NY where her family was gathered. "Our lives have been changed forever".
But he made clear that the European Union envisages a deal involving new customs and regulatory checks on goods travelling from Britain to Northern Ireland, including health and sanitary inspections for 100% of animals and animal products arriving in ports like Larne and Belfast from the rest of the UK.
A "backstop" solution to avoiding a hard border in Ireland is the major outstanding issue but a new British proposal has sparked optimism in Brussels that a Brexit deal is "very close". We've made that very clear.
"It is quite right now to expect the European Union to move in our direction and if they do match that ambition, if they do match that pragmatism, I am confident that we can still reach a deal", he said.
"We are awaiting the detail of exactly what we are going to be asked for vote for".
Earlier, amid speculation possible of ministerial resignations, Work and Pensions Secretary Esther McVey, who was not at the meeting, pointedly refused to endorse the Prime Minister's Chequers blueprint for Brexit.
"This red line is recognising that Great Britain is Northern Ireland's biggest market".
The EU's proposed solution - to keep Northern Ireland inside the bloc's single market and customs union after the rest of the United Kingdom leaves - is fiercely opposed by the Democratic Unionist Party, a pro-British Northern Ireland party that props up May's minority government.