David Davis told the BBC that Prime Minister Theresa May's letter triggering talks on Britain's departure made clear it wants to continue to work with the European Union on a range of issues, including security, for both sides.
"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".
On Thursday French President Francois Hollande backed Germany's Chancellor Angela Merkel in insisting the terms of the separation - including the so-called "divorce bill" - must be settled before they can move on to discuss a new trade relationship.
"It's not a threat", Brexit minister David Davis told BBC radio after warnings from Brussels against using security as a bargaining chip in the talks.
The status of their citizens living, working and studying in Britain needs to be guaranteed, and negotiations must also prevent a legal vacuum for European Union companies, Tusk said.
"Your Money or Your Lives", read a front page headline in the best-selling tabloid The Sun, while The Times said: "May threat to European Union terror pact".
May said Wednesday that Britain will probably have to leave the European Union police agency, Europol, after Brexit but wants to "maintain the degree of cooperation on these matters that we have now".
"It is only if we have sorted that out that we can next - and I hope soon - talk about our future relationship".
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The EU's draft Brexit guidelines were unveiled by Tusk in Malta on Friday and have been distributed to Britain's 27 EU partners.
Speaking after the release of the Council's draft negotiating guidelines Friday morning he adopted an uncompromising stance on the U.K.'s preference to hold discussions on the divorce and future trade in parallel. "We want a comprehensive deal of all aspects of our relationship with the European Union".
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Meanwhile, May published articles in five European newspapers that linked security cooperation with the Brexit talks, reiterating the controversial position taken in her article 50 letter on Wednesday.
Labour MP Owen Smith said: "Two days into a two-year negotiation and the government's lofty rhetoric is colliding with hard reality".
While a trade deal can only be formally concluded once the United Kingdom has ceased its membership, it will be possible to negotiate "an overall understanding on the framework for the future relationship" to allow for a swift agreement after withdrawal.
After May triggered Article 50 of the Lisbon Treaty on Wednesday (March 29), Britain now has two years to negotiate the terms and separate itself from the EU.
The European Council President's nine-page document states that there must be "sufficient progress" on withdrawal talks - including a "divorce bill" potentially running as high as £50bn - before negotiations on future relations begin.