European Union Chief Negotiator for Brexit Michel Barnier looks on during a news conference after a European General Affairs Ministers meeting in Brussels, Belgium, May 22, 2017. [Photo/Agencies]

BRUSSELS - It's possible for the European Union (EU) and Britain to strike a fair Brexit deal which is "far better than no deal", EU chief negotiator Michel Barnier told reporters on Monday.

"Both for the EU and the UK, a fair deal is possible, and far better than no deal, that is what I say to David today, that is why we will work all the time with the UK and never against the UK," Michel Barnier said at a joint press conference with his British counterpart David Davis, after wrapping up the opening salvo of the Brexit talks in Brussels.

His remarks obviously alluded to British Prime Minister Theresa May's catchphrase "no deal is better than bad deal."

Barnier hailed that the first session was "important", "open", and "useful indeed to start off on the right foot as the clock is ticking".

"Today we agreed on dates, we agreed on organization, and we agreed on priorities for the negotiation," he said, outlining a two-step negotiation.

"In the first step, we will deal with the most pressing issues, we must lift the uncertainty caused by Brexit; we want to make sure that the withdrawal of UK happens in an orderly manner.

"In the first step, the negotiation rounds will be broken down into three groups -- citizen rights, the single financial settlement, and other separation issues.

"These groups will report back to their respective principles during each negotiation week. David Davis and I, as chief EU negotiator, will discuss the issues together, tackle difficulties, and lift obstacles.

"Then in the second step, we scope our future partnership; we also agree on how we structure our tools."

Barnier said the two sides will have one week of negotiation every month, and use the time in between to work on proposals and exchange them.

"There will be no austerity on my side, I will display a constructive attitude firmly based on interests and support of the (EU) 27, and I will all the time seek to the continued support of the European Parliament," he said.

Echoing Barnier, British Brexit minister David Davis applauded the "very productive discussions," saying, "I've been encouraged by the constructive approach that both sides have taken."

"It was clear from the opening that both of us want to achieve the best possible outcome and the strongest possible partnership," said Davis, adding that he was happy to see that there is much common ground between the two sides.

"Ever since the referendum I have been clear that my first priority is to provide certainty to European Union citizens living in the United Kingdom and to UK citizen residents in the European Union, and I know Michele has that aspiration too.

"So now that the negotiations are started we are determined to get on with the jobs and deliver that certainty as soon as possible," he said.

He said Prime Minister Theresa May will later this week update European leaders on Britain's approach on protecting citizen rights at the EU summit slated for Thursday and Friday.

"We will then publish a detailed paper outlining our offer on (next) Monday which I believe will form the right basis on which to reach agreement," he said.

"Michel and I will meet every four weeks bringing our teams together for a number of days at a time. We hope this regular rhythm will help us progress our discussions across the full range of issues very quickly," he added.

"Today marks the start of the journey for the United Kingdom and the European Union. There's a long way to go but we're off to a promising start. We have taken the first critical steps together; now we have a shared responsibility to deliver quick and substantive progress," he said.

Regarding the future relationship with the EU, the secretary said that Britain hasn't changed its position despite the Conservative majority was wiped out after the snap election on June 8.

"We have the Lancaster House speech, the two white papers and the article 50 letter, all backed up by a manifesto -- and so it's the same as it was before," he said, reiterating that Britain will leave the single market and seek to set up a free trade arrangement with the EU.

"Similarly we'll be leaving the Customs Union... that's the only way we can develop our free trade arrangements with the rest of the world," he added.

The EU and Britain on Monday launched the long-awaited Brexit talks at European Commission's headquarters in Brussels, nearly one year after Britain voted to leave the bloc by a narrow margin on June 23, 2016.

May sent a notification letter to the EU in late March, trigge

ring a two-year countdown to Britain's withdrawal of the bloc after more than 44 years of membership.