French President Francois Hollande has told Theresa May that talks on future trade relations with the EU must come after the negotiation of a divorce deal.
Mr Hollande's stance echoed that of German Chancellor Angela Merkel as Europe presented a united front against the Prime Minister's plea for trade and divorce talks to take place simultaneously.
Failure to achieve a swift move to trade talks would threaten Mrs May's goal of completing the negotiations by the expected date of Brexit in March 2019, and could force her to seek a transitional deal lasting several years to prevent a disruptive "cliff-edge" change in trading rules.
In a statement, the Elysee Palace said Mr Hollande spoke by phone with the Prime Minister and told her it was "necessary first to initiate discussions on the arrangements for withdrawal, notably relating to citizens' rights and the obligations arising from commitments made by the United Kingdom.
"On the basis of progress being achieved on that, we would be able to open discussions on the issue of the future relations between the UK and the EU."
A statement released on Wednesday by the European Council on behalf of the 27 remaining member states said Brexit talks would "start by focusing on all key arrangements for an orderly withdrawal" and did not mention a trade deal.
Brexit Secretary David Davis played down the significance of the row over the sequencing of talks.
The Article 50 provision governing withdrawal states that the negotiations must "take into account" the future relationship along with the withdrawal arrangements, he said.
"The Commission has taken a different stance and said 'We want to deal with the departure first and the ongoing relationship second'," Mr Davis told BBC Radio 4's Today programme. "There is an area of argument over this, an area of discussion over this, which is fine."
And he added: "We are after a fully-comprehensive deal that covers trade, that covers security, covers all the aspects of our existing relationship and tries to preserve as much of it - the benefits for everybody - as we can."
Mr Davis rejected claims that Mrs May was trying to "blackmail" Brussels by linking trade and security in her letter notifying the EU of Britain's intention to quit.
Critics accused the PM of issuing a veiled threat with her warning that "a failure to reach agreement would mean our co-operation in the fight against crime and terrorism would be weakened".
The European Parliament's Brexit co-ordinator, Guy Verhofstadt, told ITV1's Good Morning Britain: "What I think is not possible is to say to the European Union 'Well, look, we will only co-operate on security if you give us a good trade deal or a good economic package'. That is not done.
"The security of the citizens is so important, the fight against terrorism is so crucial, that you cannot negotiate with something else."
And France's ambassador to the UK, Sylvie Bermann, told Today: "We are all facing the same security challenges and we all need security. So it can't be a trade-off between an FTA (free trade agreement), an economic agreement, and security."
But Mr Davis said the response from EU leaders to Mrs May's letter had generally been warm.
"Virtually all of them said spontaneously it's a very positive letter, the tone was good, and so on," he told GMB. "Guy Verhofstadt called it blackmail, let's not say everybody did."
Work and Pensions Secretary Damian Green said the row was a "misunderstanding".
The two issues had been mentioned side by side because they were "all bound up in our membership of the European Union", he said.
"It's not a threat, I think that's the misunderstanding," he told BBC2's Newsnight. "It's absolutely not a threat."
The next stage of the Brexit process sees plans set out to repatriate more than 40 years of powers back to Westminster, with the publication of details of the Great Repeal Bill.
The white paper - Legislating For The United Kingdom's Withdrawal From The European Union - sets out how the Government will deal with EU laws that cannot be easily converted.
Up to 1,000 pieces of secondary legislation are expected to be used to make technical changes - nearly as many as MPs and peers usually deal with in an entire Parliament.
Asked about his promise that the UK's trade deal would provide the "exact same benefits" as membership of the single market, Mr Davis said: "I make no apology for being ambitious about what we are trying to do."
But he acknowledged that "achieving it, of course, is a matter of negotiation, and negotiations are uncertain".
Mr Verhofstadt said the European Parliament - which has a veto on the eventual divorce deal - envisaged the Brexit process ending with an "association agreement" between the UK and the EU.
This would include both security and counter-terrorism co-operation as well as a "fair" trade deal which ensured that Britain outside the EU did not have as favourable a status as that enjoyed by members.
Downing Street said the Prime Minister had made a series of calls to European leaders, including Mr Hollande, and claimed they had welcomed her "constructive" approach.
Mrs May spoke to European Parliament president Antonio Tajani, Ireland's Enda Kenny, Poland's Beata Szydlo and Spain's Mariano Rajoy, as well as Mr Hollande.
The Prime Minister's official spokesman said she had set out that a "strong EU is in everyone's interests" and had emphasised that she wanted to remain a "close committed ally and form a deep and special partnership".
The spokesman refused to go into details of the call with Mr Hollande but insisted that the UK's position on the structure of the negotiations remained unchanged - and was set out in Article 50.
"We believe that the negotiations should take place in parallel," the spokesman said.
"It does make clear in Article 50 that the future arrangements of the country that is leaving the EU should be part of the framework for the Article 50 process."
He added that the feedback on the letter Mrs May had received from her European counterparts was that the "tone of the letter was appreciated and considered to be constructive".
But Number 10 expected that "robust positions" would be adopted.
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