Jeremy Corbyn has signalled a greater degree of support for a second referendum as he comes under pressure from his own side to respond to Labour’s poor performance in the European elections.

The Labour leader said he was “listening very carefully” to both sides of the debate after the party fell into third place behind the Liberal Democrats and also lost ground to the Greens. He said Labour’s preference would be a general election but any Brexit deal “has to be put to a public vote”.

It comes after two of his allies, John McDonnell and Diane Abbott, hardened their positions on Monday in favour of a “people’s vote”.

Tom Watson, Labour’s deputy leader, Keir Starmer, the shadow Brexit secretary, and Emily Thornberry, the shadow foreign secretary, also added to growing calls for a second referendum, with Labour campaigning to remain.

More pressure came from Dave Prentis, the general secretary of the union Unison, a major donor, who said: “If Labour is going to win the next election, it needs to understand that ambiguity and division aren’t appealing. The country needs a radical Labour government, with properly funded public services at its heart – but it won’t get that unless Labour has a clearer line on Brexit.”

However, moves to back a second referendum under any circumstances faced immediate resistance from some wings of the party – including Unite’s general secretary, Len McCluskey, and close Corbyn allies in the shadow cabinet such as the party chair, Ian Lavery, and the shadow Cabinet Office minister, Jon Trickett.

Amid the conflicting calls, Corbyn said he would consult Labour members, affiliates, MPs and shadow cabinet ministers as the party’s approach to Brexit is reviewed.

Pressed on whether he would firmly commit to a second referendum with Labour campaigning for remain, Corbyn said: “What you have from me today is a commitment that our party is listening to members and its supporters and reaching out to other parties across the House of Commons to prevent a crashing out of the EU without a deal, a commitment that the future will of course be put to a public vote as we have already proposed in parliament.”

Asked whether a public vote meant a general election or a referendum, he said: “The priority at the moment, I think, is for this government to call for a general election and actually have a general election so we can decide the future … John [McDonnell] has also pointed out, and I support this, that any final deal has to be put to a public vote and that we are prepared to do.”

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He refused to confirm that Labour would campaign to remain in the EU in another public vote. “What this party does is support an agreement with the European Union to prevent crashing out; supports putting that proposal, when agreed, to a public vote,” he said.

The demands for a second referendum grew after the party fell to third place in the European elections behind the Brexit party and Liberal Democrats. With 10 of 12 regions counted, Labour lost ground to both the Lib Dems and Greens, gaining 14.6% of the UK vote. The party also came second behind the Lib Dems in Islington, the patch of Corbyn and Thornberry.

Until now, Labour’s official line has been that a second referendum should be on the table as an option only if a general election could not be achieved, but a push for the party’s policy to shift fully to a second referendum began on Sunday with Watson, the deputy leader, criticising Labour’s “mealy-mouthed” approach to the issue, which pleases neither side.

After the polls closed, Thornberry also called for a clear shift in favour of a people’s vote, with Labour campaigning to remain.

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Abbott added to calls for a rethink. “We have to take the time to analyse the EU vote but when we come in third after the Brexit party, that is a clue something is wrong with our strategy. We need to listen to our members and take a clearer line on a public vote.”

McDonnell said in a tweet that it was time to “unite our party and country by taking [the] issue back to people in a public vote”. He subsequently clarified that a public vote could mean either a general election or referendum but conceded the former was now unlikely and the threat of a Tory no-deal Brexit was rising.

“Of course I want a general election. But I realise how difficult this is to secure. I will do anything I can to block no-deal Brexit. So yes, if as likely GE not possible, then I support going back to the people in another referendum,” he said.

Shami Chakrabarti, the shadow attorney general, had said on Sunday that it was “past midnight” for Labour to change its policy in favour of backing a second referendum.

Starmer stepped up the pressure, saying: “The only way to break the Brexit impasse is to go back to the public with a choice between a credible leave option and remain.”

David Lammy, the Labour MP for Tottenham, delivered a stinging critique of the party’s approach, telling the BBC Radio 4 Today programme it had “resuscitated the Lib Dems, handed votes to the Greens and facilitated Nigel Farage’s Brexit party”.

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He accused Labour of “hiding on the biggest issue of the day” and described it as the worst campaign he had seen in 20 years of politics.

On the other side, several senior Corbyn allies, including Lavery and McCluskey, defended the party’s position of trying to secure a “Labour Brexit” before resorting to a second referendum.

Lavery tweeted: “The country is now more polarised than ever. Very toxic very unpleasant! UK Labour we WILL NEVER turn our backs on the 48% or the 52% we will seek the real solutions that will heal society and bring together the 100%.”

McCluskey fired a warning shot at MPs agitating against Labour’s current policy, and against Corbyn. “Labour has been the only party that has sought to unite the nation on Brexit and this is an honourable objective that must not be abandoned,” he said.

In a veiled dig at Watson, McCluskey said: “Faced now with the serious prospect of a no-deal Tory prime minister, Labour must stay united and show the country that it is ready to lead. There are some rushing to advance other agendas but are doing so to undermine Jeremy Corbyn. They will be seen for what they are and never forgiven by the members.”

Labour MPs in leave-leaning seats also sounded a note of caution. Gloria De Piero, the MP for Ashfield, said backing a fresh referendum would be “an effective ending of Labour’s historic coalition of working-class, middle-class, city and non-city voters”.

Writing in the Guardian, De Piero said: “Whatever way you add up the votes, and believe me both sides in this polarised debate are frantically saying what happened means they’re right, the idea that the ‘country has moved towards’ remain is clearly wishful thinking rather than reality.”