British proposals to guarantee the rights of EU citizens living in Britain would cast "a dark cloud of vagueness and uncertainty" over the lives of millions of Europeans, the European Parliament's Brexit coordinator said.

Writing in the Guardian newspaper, Guy Verhofstadt said the differences between proposals made by the European Union and Britain to guarantee the rights of people living away from their home countries were striking, the latest sign that what should be a relatively easy part of Brexit talks was far from agreed.

The European Parliament was not convinced that Brexit would help either the European economy or its citizens.

The EU and Britain have agreed they must first deal with the rights of citizens and a financial settlement before discussing a future trade deal after Britain leaves the European Union – something Prime Minister Theresa May wants to happen quickly.

Verhofstadt said while he accepted Britain's vote to leave the EU, the European Parliament was not convinced that Brexit would help either the European economy or its citizens.

"The UK proposal only confirms this belief – falling short of its own ambitions to 'put citizens first'. If implemented, it would cast a dark cloud of vagueness and uncertainty over the lives of millions of Europeans," he wrote.

The parliament, which has the right to veto any Brexit deal, wanted the negotiations to be completed by March 30, 2019

"It was a damp squib, proposing that Europeans obtain the status of 'third-country nationals' in the UK, with fewer rights than British citizens are offered throughout the EU."

May's deputy, Damian Green, told BBC radio the government would preserve the basic rights of EU citizens in Britain, but reiterated that those rights could not be guarded by the European Court of Justice – a sticking point for the two sides.

Verhofstadt also said the parliament, which has the right to veto any Brexit deal, wanted the negotiations to be completed by March 30, 2019, adding that it would not support any extension to this deadline because European parliamentary elections were due to take place in May of that year.

"We will not support any extension to this deadline, because it would require the UK to hold European elections in May 2019," he wrote. "That is simply unthinkable."

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