The UK is offering to continue contributing troops and military assets to EU operations after Brexit as well as agreeing joint foreign policy positions with Brussels.
New proposals for a "deep security partnership" with the remaining 27-nation EU also include co-operation on international sanctions against states or terrorist organisations.
The offer is included in a policy paper setting out the UK/EU security relationship which ministers hope to agree for the period after British withdrawal.
In her Article 50 letter triggering the Brexit process in March, Theresa May warned failure to reach a deal would mean "co-operation in the fight against crime and terrorism would be weakened", in what was taken by some in Brussels as a threat to future security links.
The UK has the largest defence budget in the EU and is one of only four European Nato members to meet the target of spending 2% of GDP on defence.
Coupled with its role as a permanent member of the UN Security Council and its possession of an independent nuclear deterrent, this gives it a central role in the continent's security and makes the future relationship a matter of acute sensitivity.
The Government said, however, the new paper was a demonstration of the UK's continuing commitment to European security, making clear Britain will seek to use its assets, capabilities and influence in a security partnership that is "deeper than any other third country and that reflects our shared interest".
Speaking ahead of the paper's publication, Brexit Secretary David Davis said: "After we leave the European Union we will continue to face shared threats to our security, our shared values and our way of life.
"It's in our mutual interest to work closely with the EU and its member states to challenge terrorism and extremism, illegal migration, cyber-crime and conventional state-based military aggression.
"Today's paper highlights Britain's world-class diplomacy and defence capabilities, our leading contribution to international development and our desire to continue to use these as part of a deep and special partnership with the EU."
Foreign Secretary Boris Johnson said: "As we leave the EU, the UK's commitment to European security is undiminished.
"We will pursue a global foreign policy and continue to work in partnership with our neighbours to promote peace, democracy and security in our continent and across the world."
Labour MP Chris Bryant, a leading supporter of the Open Britain campaign against a hard Brexit, said: "The Government's intention to continue to share a deep foreign policy and security relationship with the EU in future is welcome, but it makes a mockery of their threat to leave the EU with no deal at all.
"Doing so would overnight end our security relationship with Europe, putting our citizens and theirs at risk.
"It is high time the Government dropped its absurd no-deal threat."