"We are going to continue to oppose any idea of an EU army or an EU army headquarters which would simply undermine NATO," Fallon said at a meeting with his 27 counterparts in Bratislava, where European Union leaders earlier this month agreed to step up joint military efforts.
Asked if Britain could veto the plans while it still remains a member of the European Union ahead of Brexit, Fallon said: "There is no majority here for a EU army."
"There are a number of other countries who believe with us that cuts across the sovereignty of individual nation states," he added.
"We agree Europe needs to do more, it's facing terrorism, it's facing migration, but simply duplicating or undermining Nato is the wrong way to do it."
EU leaders met without Britain in the Slovakian capital on September 16 to discuss plans to move forward in the wake of the stunning British vote to leave the bloc on June 23.
They agreed on a six-month roadmap to create a new "vision" for the EU, including beefed up defence cooperation, which Britain has always opposed.
Fallon insisted however that Britain would continue to contribute to European defence as a member of NATO.
"We are leaving the European Union but we remain committed to the security of Europe and putting more troops into Estonia or Poland next year."
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