As campaigning ramps up ahead of next month's general election, he warned that leaving the EU would leave the UK a "second-rate player".

In a speech, he also said Brexit would likely mark the "real end of the British Empire".

He is due to step down from his role next month, having held the post for five years.

Mr Tusk's intervention comes as Conservative leader Boris Johnson said the UK Parliament was "paralysed" and had refused "time and again to honour the mandate of the people and to deliver Brexit".

Meanwhile, the UK has continued to refuse to put forward a candidate for the next European Commission, which is due to take office next month if approved by MEPs.

The BBC understands the UK's EU ambassador has written to the Commission saying that a candidate will not be put forward due to the election.

In the letter, Sir Tim Barrow is understood to say pre-election rules prevented ministers from putting forward nominees for jobs at EU institutions until after polling day.

However, he is understood to have insisted the UK does not want to stop the Commission being formed as soon as possible.

Mr Johnson is hoping to win a majority in 12 December's election so that he can take the UK out of the EU on 31 January with the deal he negotiated with Brussels.

But Labour is promising to renegotiate that deal and put it to a referendum, with the option of remaining in the EU, if it wins the election - and smaller opposition parties are campaigning to Remain.

Brexit 'extra time'

Speaking at the College of Europe in Bruges, Mr Tusk said: "Brexit may happen at the beginning of next year.

"I did everything in my power to avoid the confrontational no-deal scenario and extend the time for reflection and a possible British change of heart".

"The UK election takes place in one month. Can things still be turned around?

"The only words that come to my mind today are simply: Don't give up.

"In this match, we had added time, we are already in extra time, perhaps it will even go to penalties?"

Donald Tusk's term of office ends in a few weeks' time.

Which means he's prepared to brave accusations that he's interfering in the general election.

And that he feels free to challenge the sense developing among the rest of the EU, that it would be better if the UK left as soon as possible.

Speaking at the College of Europe in Bruges tonight, he quoted the philosopher Hannah Arendt to encourage those campaigning for Britain to remain.

His message was simply not to give up.

The EU has accepted an extension to the Brexit deadline, meaning the UK is now due to leave at the end of January 2020.

Mr Tusk has repeatedly hinted he would like to see the UK stay in the bloc - but his comments, in the midst of an election campaign - are likely to be controversial.

He acknowledged this in his speech, adding his remarks were "something I wouldn't have dared to say a few months ago, as I could be fired for being too frank".

He added that a "longing for the Empire" could be heard in the voices of Brexiteers who strive to make the UK "global again" through leaving the EU.

"But the reality is exactly the opposite. Only as part of a united Europe can the UK play a global role," he added.

"One of my English friends is probably right when he says with melancholy that Brexit is the real end of the British Empire."

Mr Tusk is due to stand down from his role on 1 December, when he will be replaced by former Belgian PM Charles Michel.