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European Council President Donald Tusk has suggested that the UK should stay in the EU, after the prime minister's Brexit deal was rejected in parliament, BBC News reports.

"If a deal is impossible, and no one wants no deal, then who will finally have the courage to say what the only positive solution is?", he tweeted.

MPs voted by 432 votes to 202 to reject the deal, which sets out the terms of Britain's exit from the EU on 29 March.

EU officials and politicians have reacted with dismay to the result.

European Commission President Jean-Claude Juncker warned that time was running out for the UK to strike a deal.

"I urge the United Kingdom to clarify its intentions as soon as possible. Time is almost up," he said shortly after the result was announced.

"The risk of a disorderly withdrawal of the United Kingdom has increased with this evening's vote," he added.

The EU's chief Brexit negotiator Michel Barnier said the UK had to decide on its approach.

"It's now up to the British government to say what the next stage is," he said. "The EU will remain united and determined to find a deal."

German Finance Minister and Vice Chancellor Olaf Scholz said Tuesday was a "bitter day for Europe".

"We are well prepared, but a hard Brexit would be the least attractive choice, for the EU and [UK]," he said.

"The pressure is mainly on them," French President Emmanuel Macron said of the UK.

He warned that a transition period is essential because a no-deal Brexit would be damaging.

"We will have to negotiate a transition period with them because the British cannot afford to no longer have planes taking off or landing at home," he said.

In a short statement, the Irish government said it would ramp up preparations for the UK leaving without an agreement.

"Regrettably, the outcome of tonight's vote increases the risk of a disorderly Brexit," it said.

"Consequently, the government will continue to intensify preparations for such an outcome."