European Council president Donald Tusk has rejected a call to intervene to secure the rights of EU nationals living in the UK - and Britons in the EU - before formal Brexit negotiations begin next year.
A group of 50 mainly Conservative MPs from the European Research Group has written to Mr Tusk urging him to end the deadlock in the row over reciprocal rights.
The letter accuses the European Commission's lead negotiator Michel Barnier of being "worryingly indifferent" to the concerns of British and EU citizens living in one another's territories, causing "anxiety and uncertainty".
But in a scathing reply, Mr Tusk dismissed the criticisms of Mr Barnier and said talks on reciprocal rights could only begin once the UK Government triggers Article 50 marking the start of the formal withdrawal negotiations.
"It is a very interesting argument, the only problem being that it has nothing to do with reality," he wrote.
"Would you not agree that the only source of anxiety and uncertainty is rather the decision on Brexit? And that the only way to dispel the fears and doubts of all the citizens concerned is the quickest possible start of the negotiations based on Article 50 of the Treaty?"
In their letter, organised by Conservative backbencher Michael Tomlinson, the MPs said that finding a quick solution to the issue was the "only just and humane thing to do" and that anything else would be "unworthy of Europe's common values".
"Human beings are not cards to be traded 'tit for tat' in a political playground. People must come before institutions and adherence to process, European or otherwise," they wrote.
"No European expatriate's livelihood and family should be held hostage in this way, whether from the UK or the EU27."
However Mr Tusk said that while the EU stood ready to start negotiations, it was a matter for the UK when it invoked Article 50.
"Just like you, I would like to avoid a situation where citizens become 'bargaining chips' in the negotiation process," he wrote.
"In order for this not to happen, we will need precise and comprehensive solutions, which, other than nice-sounding expressions, will provide citizens with genuine guarantees of security."
The row came amid reports German chancellor Angela Merkel rebuffed an attempt by Theresa May - who has long made clear she would like the issue resolved outside the main Brexit negotiations - to find an early settlement.
The Politico website reported that Mrs Merkel rejected a proposal by the Prime Minister guaranteeing reciprocal rights for both groups when they met in Berlin earlier this month.
Downing Street refused to be drawn on the claims, but confirmed that the Government would like to see an "early agreement" on the issue.
"We have been very clear that we will guarantee the rights of European citizens in this country provided that the rights of British citizens are similarly protected across the EU.
"We have been very clear that we would like to see an early agreement on that, but we need to have a dialogue with the 27 member states."
Mrs Merkel is likely to come under pressure from German voters to take a tough line with the UK in the Brexit negotiations, according to a new survey.
The Guardian reported that a poll conducted by the Korber Foundation found 58% of Germans thought Mrs Merkel - who faces federal elections next year - should not compromise in discussions on Britain's withdrawal from the EU.
Support for a hardline approach was particularly strong among the German chancellor's own CDU with 65% saying she should not give ground to the UK.
Meanwhile Poland's foreign minister Witold Waszczykowski, who held talks with Boris Johnson in London on Monday, suggested that Brexit may never happen.
"It is in our interest that Britain remain an EU state as long as possible and pay contributions as long as possible," he told the Polish newspaper Rzeczpospolita.
"Brexit will not take place earlier than in two to three years, if it takes place at all. In the next three years there is no need to treat Britain as a child with special needs, which is stigmatised and marginalised."