Taoiseach Leo Varadkar has claimed that the European Union would be flexible in Brexit negotiations if the UK could relax from some of its red line issues in the wake of last Friday’s Chequers statement.

The UK government had agreed Theresa May's plan for retaining strong economic ties to the EU even after Brexit at the Chequers meeting.

However, Foreign Secretary Boris Johnson and Brexit Secretary David Davis have since resigned, with Mrs May saying they differed on the way forward.

Speaking in the Dáil, Mr Varadkar said: "If the United Kingdom was able to relax from some of its red lines, then the European Union could be flexible too. I think we are now entering into that space."

During Leaders' Questions, Fianna Fáil leader Mícheál Martin said yesterday's drama in London should not distract from the key message in the Chequers statement.

He said the statement was in line with reality that rendered it impossible for hardline Brexiteers to stay in office.

The Cork TD said credit should be given to Theresa May for navigating the Chequers agreement.

He said that Ireland exports hugely to the UK and warned that studies predict negative outcomes for SMEs, agri-food sector and businesses on the border.

Mr Martin said Ireland must retain a key focus on what is optimal for the country, and asked if the Taoiseach accepted that the east-west relationship was critical.

He also asked if Mr Varadkar accepted that the Chequers statement represented a credible basis to proceed.

The Taoiseach noted the resignations of David Davis and Boris Johnson. He said they were internal matters for the UK government and the Conservative party.

Mr Varadkar said he spoke to Mrs May for half an hour on Saturday following the three-page Chequers statement, adding that the more than 100-page White Paper is due to come out this week.

He said regular contact was being kept with London and he was awaiting the publication of the white paper.

Mr Varadkar said: "The Chequers statement is welcome. I believe it can input into the talks on the future relationship. We would like to see the White paper first ... I imagine there will be a lot more in a 100-page paper than there is in a three-page paper.

"On the face of what we see, I think it can input into the talks of the future relationship. I believe it is welcome.

"If the United Kingdom was able to relax from some of its red lines, then the European Union could be flexible too. I think we are now entering into that space."

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The Taoiseach added that Ireland would still need a backstop and the future relationship treaty would have to be agreed by each parliament in each member state and that was why we must have a backstop.

"Do you believe the Chequers statement represents a credible pathway to negotiation?" asked Mr Martin.

The Taoiseach said he believed that the Chequers statement was "a valuable input" and it may produce a path to better negotiations. However, he warned: "I don't think it is a solution on its own."

Sinn Féin leader Mary Lou McDonald said it was essential that Ireland obtained legal guarantees to underpin the backstop agreed in December aimed at avoiding a hard border between Ireland and Northern Ireland. 

"The backstop agreed in December is the bottom line" she said.

"So Taoiseach you can’t concede, there can’t be any flexibility or no blurring or softening of the lines on this matter. You can’t continue to accept bad faith from the Tory government" she said.

"I don’t think that we can allow these matters to slip into the hazy days of the Summer and sit back and hope for the best".

Ms McDonald also said there was a need for a special EU leaders' summit to be held on the subject of Brexit in September.

The Taoiseach said he was not hung up on legal texts around the backstop.

"It's about the outcome, it's about achieving a legally binding agreement that there can be no hard border with Northern Ireland," he said.

"It's not about the legal text, it's about what happens on the ground."

On the proposal for a special EU leaders’ summit to discuss Brexit, he said "that is possible".

Mr Varadkar said: "The 28 heads of state and government are meeting in Salzburg in September. I discussed with [Austrian] Chancellor [Sebastian] Kurz the possibility of upgrading that to a formal summit on Article 50, but we will make that judgement closer to the time."

Labour leader Brendan Howlin said the UK Labour party wanted to maintain the single market and full membership of the customs union for four years while Mrs May wanted to leave both by March next year.

He said there was a golden opportunity for a special summit on 20 September as part of the Austrian presidency to get clarity on the backstop.

He asked if the Taoiseach could get the Irish backstop agreement formally tabled on the agenda by the Austrian presidency for that summit.

The Taoiseach agreed with Mr Howlin's analysis and said that he discussed the Salzburg summit with Chancellor Kurz and it was an option that would have to be discussed.

Mr Howlin said a deadline of a settlement on the backstop issue in September was infinitely better than leaving it in the general pot of discussions for the October summit.

The Taoiseach said it was absolutely his preference to have an early agreement and have it as soon as possible, but he is not going to make concessions in order to get agreement as soon as possible.

Mr Varadkar said the October deadline was put in place to allow the UK parliament time to ratify any agreement.

This morning, Tánaiste and Minister for Foreign Affairs Simon Coveney briefed the Cabinet on the state of the Brexit negotiations in light of recent political developments in the UK.

Additional reporting Justin McCarthy, Martina Fitzgerald