The EU has said it is willing to revisit the proposal of a Northern Ireland-only backstop to break the Brexit deadlock.
The President of the European Parliament, David Sassoli, said there would be no agreement without a backstop in some form.
But on Wednesday, Prime Minister Boris Johnson ruled out an NI-only backstop.
The UK is due to leave the EU on 31 October without a deal unless both sides can reach a compromise.
Mr Sassoli was speaking at a press conference after a meeting of the EU Conference of Presidents with EU chief Brexit negotiator Michel Barnier.
UK officials have been in Brussels for meetings this week with Mr Barnier’s team.
The backstop has proved to be the most contentious part of the Brexit negotiations.
It is the insurance policy to avoid a hard border between Northern Ireland and the Republic of Ireland after Brexit, unless and until another solution is found.
MPs had voted down the backstop and withdrawal agreement negotiated by Theresa May, which would have kept all of the UK in a “temporary customs territory” with the EU and would have seen Northern Ireland also continuing to follow other EU rules.
The Democratic Unionists (DUP) had opposed it, saying it would create a border down the Irish Sea and risk the future of the union.
There had been speculation in recent days that the UK was considering returning to the idea of a Northern Ireland-only backstop, which had originally been proposed by the EU in the early stages of the negotiations in 2017.
The DUP had insisted it and No 10 would not back such a proposal as it would not have “unionist consent”.
After talks with Boris Johnson on Tuesday, the DUP said it was exploring all-island “arrangements” on food standards and animal safety as part of a solution to replace the backstop.
But on Thursday, the EU said it was “unhappy” that it had still not received any credible proposals from the UK.
Mr Sassoli said a draft resolution, to be considered by the European Parliament next week, states its preparedness to return to the “original EU proposal” of an NI-only backstop.
“You can’t have an agreement without the backstop, it couldn’t really be any clearer,” he added.
‘Firmness and clarity’
He added that the signal the EU is getting is that there is “no initiative” from the UK right now that could reopen the Brexit negotiations.
The next EU summit is due to take place on 17-18 October, just several weeks before the UK is due to leave the EU on 31 October.
The prime minister has insisted he will not ask the EU for another extension to the deadline, and said the UK would be ready to leave with or without a deal.
He has said he hoped a deal could be reached and that he has an “abundance of proposals” to replace the backstop – but has not detailed what they might be.
The Irish government has said it would also be willing to look at a “Northern Ireland-specific solution”.
Mr Sassoli said the EU had “reached a moment where we need to express our positions with firmness and clarity”.
What was the NI-only backstop?
Proposed by the EU, it would have kept Northern Ireland in the EU’s customs union, which would have meant applying EU tariffs for goods entering NI from outside the EU customs union – including Great Britain.
It would also have applied EU single market rules for goods and animal products in Northern Ireland.
This would have got rid of the need for checks at the Irish border, but would have led to checks on goods passing between Northern Ireland and Great Britain.
It was criticised by the DUP and other unionist parties for “creating a border in the Irish Sea” and posing a risk to the union.
In February 2018, Theresa May said no prime minister could back such a proposal.