Video report by ITV News Europe Editor James Mates
There is "no room whatsoever for renegotiation" of the UK's Brexit deal, European Commission President Jean-Claude Juncker has said as Theresa May holds emergency talks with EU leaders.
Mr Juncker said there could be further "clarifications and interpretations" but the Withdrawal Agreement "will not be reopened".
Mrs May held talks with her Dutch counterpart Mark Rutte before meeting German Chancellor Angela Merkel in Berlin and will later head to Brussels after her decision to cancel a vote in the House of Commons on her Brexit deal left Westminster in turmoil.
The prime minister is trying to obtain reassurances about the UK's exit deal, in particular the Irish border backstop, after admitting she faced a "significant" Commons defeat on it in its current state.
Her spokesman said Mrs May will bring the deal back to the Commons "before January 21".
Tory Brexiters and the DUP, who prop up Mrs May's Government, are fiercely opposed to the backstop, which would see the UK obey EU customs rules after a transition period if a wider trade deal has not been agreed by then.
But European Council president Donald Tusk has already insisted there was no question of reopening negotiations, including on the backstop, and Mr Juncker backed up that statement on Tuesday morning.
Mr Juncker said the Withdrawal Agreement is the "only deal possible".
MEPs applauded as he said: "There is no room whatsoever for renegotiation, but of course there is room if used intelligently, there is room enough to give further clarifications and further interpretations without opening the Withdrawal Agreement.
"This will not happen: everyone has to note that the Withdrawal Agreement will not be reopened."
Mr Juncker said the Irish backstop was the "big problem", explaining: "We have a common determination to do everything to be not in the situation one day to use that backstop.
"But we have to prepare: it's necessary for the entire coherence of what we have agreed with Britain and it is necessary for Ireland. Ireland will never be left alone."
ITV News Correspondent Angus Walker in Brussels
EU leaders will meet for a summit on Thursday where Brexit will again be on the agenda after the latest developments.
However Mr Tusk tweeted they "will not renegotiate the deal, including the backstop".
"But we are ready to discuss how to facilitate UK ratification," he said. "As time is running out, we will also discuss our preparedness for a no-deal scenario."
On Wednesday, Mrs May will travel to Dublin to meet with Taioseach Leo Varadkar, likely for discussions over the backstop and the issue of the border between Northern Ireland and the Republic.
Following this engagement, Mrs May will then fly on to Brussels ahead of the European Council meeting on Thursday, but no further meetings in the Belgian capital have yet been announced.
The Prime Minister is also planning to speak by phone with Austrian Chancellor Sebastian Kurz on Tuesday afternoon while she is in Brussels for meetings with Donald Tusk and Jean-Claude Juncker.
As Mrs May travelled to Europe, Commons leader Andrea Leadsom suggested that the prime minister was seeking changes that would give Parliament an additional "democratic ability to decide".
She told the BBC Radio 4's Today programme: "That might include an addendum to the Withdrawal Agreement that sets out that Parliament will vote prior to going into a backstop, should that prove necessary, and potentially that the EU parliament and UK parliament must vote every year thereafter to provide that legitimacy for the UK to stay in the backstop, should that prove necessary.
"So there are plenty of options for the PM to talk to the EU about that don't involve reopening the Withdrawal Agreement, but that would provide the legal text as a part of the Withdrawal Agreement, through perhaps an addendum."
MPs have secured an emergency debate on Mrs May's decision to pull the Commons vote and opposition leaders have used a joint letter to accuse her of showing contempt for Parliament.
But Labour leader Jeremy Corbyn is yet to bow to pressure to call a vote of no confidence in the Government.
More than 30 MPs, 15 peers and five MEPs have signed a letter urging the Labour leader to table a vote this week.
Shadow business secretary Rebecca Long-Bailey suggested Labour would not table a no-confidence motion until Mrs May returns from her talks with Brussels.