The leaders reiterated that a no-deal Brexit is the "worst possible outcome" and if it happens it will not be the choice of the EU.
Their comments come against a backdrop of fury over the suspension of the UK parliament for five weeks and publication of a 5-page government Yellowhammer document, an assessment of a reasonable worst-case scenario in the event of a no-deal Brexit.
The UK is due to leave the EU on 31 October, a deadline the British Prime Minister Boris Johnson says he intends to honour "come what may."
On Friday, S&D group leader Iratxe García Pérez said, "A no-deal Brexit would be bad for everyone but a disaster for the UK. That is not just our view, it is clear from the UK government’s own assessment of what will happen following a no-deal departure, with severe delays at ports, medical supplies being disrupted, and food prices increasing."
"It would also lead to even more uncertainty for the millions of EU27 citizens living in the UK and UK citizens living in other EU countries."
She added, "Today all major pro-EU forces in the Parliament have stated that we would support an extension to avoid this outcome. If the UK needs more time to hold a general election or a new referendum then this will be granted. We have always seen Brexit as a historic mistake and would still welcome it if the decision was reversed."
"Today all major pro-EU forces in the Parliament have stated that we would support an extension to avoid this outcome. If the UK needs more time to hold a general election or a new referendum then this will be granted" S&D group leader Iratxe García Pérez
"We urge Boris Johnson and his government to live up to the promises they have made and automatically grant rights to EU nationals living in the UK. People should not pay the price for their politicians’ failings, this is why our group supports ring-fencing citizens’ rights in all circumstances," she added.
Her remarks were endorsed by another senior MEP, Pedro Silva Pereira, interim member of Parliament’s Brexit Steering Group, who added, “Even if we regret Brexit, our group has worked in a responsible way to mitigate its worst consequences and ensure that the UK leaves the EU in an orderly way. Therefore, we will support an extension of Article 50 if needed to avoid a catastrophic no-deal scenario."
"Our priorities remain to see that the rights of EU citizens are guaranteed in all circumstances and to protect the peace process in Northern Ireland. We are deeply concerned by the difficulty EU citizens, some of whom have lived in the UK for decades, have had in receiving settled status from UK authorities."
"This, combined with confusing and contradictory statements from the UK Home Office on ending freedom of movement after October 31, are causing stress and uncertainty for millions of people who have chosen to build their lives in the UK."
He continued, "Our group is also clear that we will never accept any Brexit deal that could threaten or undermine the EU’s hard won labour rights or environmental standards."
Parliament’s group leaders adopted a resolution on Thursday which says that crashing out on 31 October will "entirely be the responsibility" of the UK government. Moreover, the resolution says that suspension of the UK parliament makes a no deal exit "more likely."
Elsewhere, the EU's chief Brexit negotiator told political leaders in the European Parliament on Thursday that he could not say whether contacts with the UK government would result in a deal by mid-October.
"We will support an extension of Article 50 if needed to avoid a catastrophic no-deal scenario" Pedro Silva Pereira MEP
Michel Barnier, in a speech to MEPs, suggested that negotiating a new Withdrawal Agreement remained uncertain despite discussions between Boris Johnson's team and the EU.
"I cannot tell you objectively whether contacts with the government of Mr Johnson will be able to reach an agreement by mid-October," he said.
On yet another whirlwind day in British politics, Commons Speaker John Bercow, in a speech late on Thursday, vowed "creativity" in the UK Parliament if Boris Johnson ignores a law designed to stop a no-deal Brexit.
Bercow, due to stand down next month, also said in the speech that the only possible Brexit was one backed by MPs.
A new law, passed before the suspension of Parliament, forces the Prime Minister to seek a delay until 31 January 2020, unless a deal or no-deal exit is approved by MPs by 19 October.
Meanwhile, the case for a second referendum on the UK’s EU membership before a general election "is not only overwhelming but also gaining more support in parliament", according to former Conservative MEP Brendan Donnelly.
The possibility of a so-called "people’s vote" has been flagged most recently by senior Labour MP Tom Watson and Donnelly told this website that a second referendum is the only way to resolve the impasse on Brexit.
"I cannot tell you objectively whether contacts with the government of Mr Johnson will be able to reach an agreement by mid-October" Michel Barnier
Donnelly, now director of The Federal Trust, said, "Despite Boris Johnson’s insistence that Brexit should be resolved through a general election, recent data suggests that an early poll would fail to break the impasse."
Analysis conducted on behalf of Channel 4 News in the UK suggests that the Conservatives would end up with the same number of seats as in 2017.
The reason for this, says Donnelly, is that despite winning some seats from Labour, the Conservatives would lose others to the Brexit party and the Liberal Democrats.
He said, "It is difficult to imagine any plausible electoral outcome that will contribute in any meaningful way to solving the network of conundrums thrown up by Brexit. It is all too easy to imagine outcomes that will make matters a great deal worse."
Donnelly argues that a more attractive option would be to stage a referendum before any general election.
The view that a referendum should be prioritised over a general election has received strong support from Watson, the Deputy Leader of the Labour Party.
In a speech in London, Watson said, "The only way to break the Brexit deadlock once and for all is a public vote in a referendum. A general election might well fail to solve this Brexit chaos."
However, Watson’s position is at odds with the position of the Labour Party leader, Jeremy Corbyn. Speaking in Walsall last week, Corbyn emphasised that the Labour Party position is to prevent a no-deal Brexit, then hold a general election and only then to put any Withdrawal Agreement to a public vote (with the choice to remain).
Asked about Tom Watson’s speech he simply said: "It’s Tom’s view … I don’t accept it, I don’t agree with it."
Donnelly says, "There is a substantial existing body of opinion within the Labour Party favourable to a referendum. But it is interesting to note that a number of dissident Conservatives, most notably Oliver Letwin and (possibly) Philip Hammond, are now moving in this direction."
"Liberated of the shackles imposed by membership of a disintegrating Conservative Parliamentary Party, these expelled MPs now have an unusual opportunity to make a decisive contribution to the restructuring of British politics."