Hollande has joined forces with Angela Merkel by rejecting UK Prime Minister Theresa May's request that Brexit talks can run parallel to negotiations over a future trade deal.
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.
Tusk will meet May in London ahead of an European Union summit on Brexit, which will not include her, on April 29.
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.
If Britain remains a part of the European Union single market for a time after Brexit, it would also have to respect all "four freedoms", which would mean accepting open immigration from the continent.
In a worst-case scenario, Britain could end up having even less ties with the EU than Switzerland, which has never planned to join the European Union.
One particularly tricky aspect for May will be demand to spell out the UK's relationship with the European Court of Justice early in the talks, and how EU law applied to the exit deal, during any interim arrangement, and in the longer term.
US sanctions North Koreans linked to weapons of mass destruction
Trump said while he believes in alliances and partnerships, they "have not always worked out very well" for the U.S. The North also denounced ongoing military drills involving American hardware and troops in South Korea.
"It is only if we have sorted that out that we can next - and I hope soon - talk about our future relationship".
But Liberal Democrat leader Tim Farron, who campaigned against Brexit, said the guidelines showed "the strength of the EU in these negotiations and the carelessness of the United Kingdom government in isolating themselves from our European allies".
Deutsche also criticised Mrs May's use of security intelligence as part of Britain's negotiating stance and said it is a "negative approach".
"We want a deal, and she was making the point that it's bad for both of us if we don't have a deal", Davis told the BBC.
With the two-year clock ticking on Britain's departure from the European Union, Spanish nurse Joan Pons and millions of other EU citizens living in the United Kingdom are facing an uncertain future. "You start at five o'clock in the morning, up to 10 hours every day, six days a week", said Szomoru, who came to Britain 10 years ago and started out picking strawberries before being promoted to her current job.
A senior European Union diplomat likened the insistence on sequencing to the repetition by the 27 since Britain's referendum that there could be "no negotiation before notification" - a stance they believe forced May to accept the two-year deadline set by Article 50, which she might otherwise have tried to avoid.
"You can not use the security of our citizens in a negotiation and say 'oh, yeah, we're going to only cooperate on the security of our citizens in the fight against terrorism if we have a good trade deal,"' he said.