"What the UK is offering will be unprecedented in its breadth, taking in cooperation on diplomacy, defence, security and development, and depth, in terms of the degree of engagement that the UK and the EU should aim to deliver," the government said in a policy paper.
"The UK is unconditionally committed to maintaining European security," it said.
The government emphasised that "NATO will continue to be the cornerstone" of its security upon leaving the EU in March 2019 but that Britain would seek a UK-EU relationship that is "deeper than any third country partnership".
The Guardian newspaper said the latest paper "strikes a more positive note about EU defence and foreign policy matters than expected".
Prime Minister Theresa May warned in March -- after triggering Article 50 and starting the divorce proceedings -- that failing to reach a new trade deal once Britain leaves the bloc could damage cooperation against crime and terrorism.
The government denied it was implying a threat, saying it was a fact that unless Britain agreed to continue its security cooperation projects, including with the Europol law enforcement agency, then it would leave them after Brexit.
"What we are doing -- and everybody has asked for this -- is to set out how we see the new partnership the day after Brexit."
"We want to fight terrorism together. It's vital. We are not making threats," he said.
The position paper -- the twelfth to be released by the British government -- does not mention cooperation on cross- border crime or whether it will remain a member of Europol.
The UK government said today that the next round of Brexit negotiations had been delayed a week and would now start on September 25.
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