Mogherini's comments came in response to a veiled threat from British Prime Minister Theresa May that the EU's security could be compromised if London-Brussels Brexit negotiations sour.
"Starting parallel talks on all issues at the same time, as suggested by some in the United Kingdom, will not happen", he said, adding that the EU-27 will assess "probably [in] the autumn if sufficient progress has been achieved".
Prime Minister Theresa May today reached out to the European press to strike a tone of friendship and send out a message that Britain's exit from the EU was not an attempt "to do harm" to the bloc.
However, her hopes to discuss separation terms and a "bold and ambitious" free trade agreement at the same time have been knocked back by German chancellor Angela Merkel and French president Francois Hollande.
British Foreign Secretary Boris Johnson, in Brussels as North Atlantic Treaty Organisation ministers met US Secretary of State Rex Tillerson, said London was committed to European security and that it was "not some bargaining chip" in the Brexit talks. But he also said the European Union will not punish the U.K.in the exit talks, and that the so-called Brexit is punitive enough.
April 27 - European Union affairs ministers of the 27 - the General Affairs Council or GAC - meet in Luxembourg to prepare EU27 summit.
She said Britain must first work out how to unwind its relationship with the European Union and pay its debts: "Only then, later, can we talk about our future relationship".
The EU's draft Brexit guidelines were unveiled by Tusk in Malta on Friday and have been distributed to Britain's 27 EU partners.
The fate of three million European Union citizens living in Britain and one million British people within the bloc's nations is at the top of leaders' agenda.
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But the draft negotiating guidelines released Friday set out a "phased approach" to the talks from the EU27.
One possibility may be to set Britain a goal of showing it is getting on with agreeing the outline divorce before allowing trade talks to start.
Among the criticisms aimed at May, the EU's chief Brexit negotiator, Guy Verhofstadt, lablled the tactic "blackmail", and warned that security should not be used as a bargaining chip.
'We already miss you, ' Tusk said.
'It is my fierce determination to get the right deal for every single person in this country, ' she said.
"We are thinking of moving to Australia", a 45-year-old Spanish nurse from Barcelona, who is married to a Spanish doctor, told AFP.
But in its draft negotiating guidelines for the upcoming withdrawal talks, the Council did not rule out trade talks beginning within the two-year period leading up to Brexit.
Negotiations on future trade relations between the United Kingdom and EU can only begin after "sufficient progress" has been made on disentangling Britain from the ties and obligations of its 44-year membership, the European Council has said.
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