The UK would be welcome to stay in the EU if it changed its mind about Brexit, Donald Tusk has suggested.
The European Council President told MEPs that the UK would leave the bloc unless it had a "change of heart".
"We haven't had a change of heart. Our hearts are still open for you."
The comments were welcomed by MPs who want a referendum on the final Brexit deal but Environment Secretary Michael Gove said the British public had voted in record numbers to leave the EU.
"We have a great future outside the European Union and we should be embracing that," he said.
The government has said there will be no second vote ahead of the UK's exit in March 2019.
Labour leader Jeremy Corbyn has also dismissed the idea while insisting that MPs have a "meaningful vote" in Parliament on the terms of the withdrawal agreement.
Former UKIP leader Nigel Farage has said the prospect of a second vote cannot be ruled out, although he was confident it would return a larger margin for Leave than in 2016 - when 17.4 million people voted for Brexit.
The EU, he told BBC World Service, was intent on "putting something on the table so unattractive to Britain that Parliament will vote for us to have a second referendum".
As it stands, the UK is due to leave the EU in March 2019.
The two sides reached a deal on so-called "divorce issues", including money and citizens' rights, in December and talks are now moving onto transitional arrangements and future co-operation.
Revised draft EU guidelines obtained by several UK newspapers suggest the EU is toughening its stance on what changes the UK can make on immigration, trade and fishing during a roughly two year transition period.
Speaking in the European Parliament in Strasbourg, Mr Tusk said he believed the other 27 EU members would maintain their unity when the talks resumed in March.
"The hardest work is still ahead of us, and time is limited," he said.
"If the UK government sticks to its decision to leave, Brexit will become a reality - with all its negative consequences - in March next year. Unless there is a change of heart among our British friends.
"Wasn't it David Davis himself who said 'if a democracy cannot change its mind, it ceases to be a democracy'.
"We, here on the continent, haven't had a change of heart. Our hearts are still open to you."
Former Lib Dem leader Nick Clegg, who has said Parliament should have the power to reject any deal reached and force ministers back to the negotiating table, welcomed Mr Tusk's remarks.
Donald Tusk is right. The world has moved on since June 2016. Brexiteers keep banging on about freedom, but one of the greatest freedoms is the freedom to change your mind.— Nick Clegg (@nick_clegg) January 16, 2018
Labour MP Daniel Zeichner, a supporter of the Best for Britain group, which was launched last year by pro-EU campaigner Gina Miller, said the option to remain in the EU must be kept open.
"We are stronger together, and it becomes increasingly clear that the current path is extremely damaging," he said.
But Leave Means Leave, which grew out of the Vote Leave campaign during the 2016 referendum, said Brussels had a history of not listening to the views of voters.
"Donald Tusk and Jean-Claude Juncker need to accept that Britain is a democracy - something the EU knows very little about," said its co-chair Richard Tice.
"The British people voted to leave the EU and this decision will not be reversed, despite their best efforts."
Mr Tusk's sentiments were also dismissed by prominent Brexiteers in the European Parliament.
So Donald Tusk has clambered aboard the 2nd Referendum bandwagon. Usual cynical EU tactic when a free people vote the "wrong" way. But our referendum was the decisive verdict and the Govt is honour bound to implement it. So jog on Don. https://t.co/AMOgv4SQri— Patrick O'Flynn (@oflynnmep) January 16, 2018
If Tusk and Juncker truly wanted Britain to stay in the EU, they'd propose a looser arrangement. Their refusal to contemplate such a thing explains why we're leaving.— Daniel Hannan (@DanielJHannan) January 16, 2018