By Andrea Shalal

BERLIN (Reuters) - Germany's defense minister said on Monday the European Union must modernize its military defense and security to match NATO's drive to beef up its own security forces in the wake of a major Russian build-up.

France, Germany, Italy and Spain are calling for a common European defense policy after Britain's vote to quit the bloc, an initiative that marks the EU's biggest push since the 1990s.

"We have seen an enormous modernization drive by NATO over the past three years because of the Kremlin's behavior," Ursula von der Leyen told a security conference hosted by the conservative Christian Democrats.

"That was correct and important, but I believe that we must invest at the least same energy into a modernization of the European security and defense union," she said.

Von der Leyen, keen to assuage concerns raised by the United States and Britain, said the increase should occur "knowing that one cannot build up competition between the two bodies, but that they should work in a complementary fashion".

For instance, she said, the EU had a clear mission in working with Africa to stem the steady flow of migrants crossing the Mediterranean Sea, but that was not NATO's job.

"I see a big mission for the European Union, which must work for a solution together with the African countries," von der Leyen said. "But to do that, it must better organize and bundle the many instruments it has in the civilian and military realms, actually implement them, and offer a joint European response."

In a joint letter, Germany, France, Italy and Spain have argued that the EU should be able to respond to external crises without the guiding hand of the United States.

Proposals include increasing European spending on military missions, jointly developing assets such as helicopters and drones, expanding peacekeeping abroad and building stronger defenses against state-sponsored hackers.

NATO, and especially the United States, has long argued that Europeans should increase defense spending and strengthen their militaries to ensure their own defense.

EU defense ministers will hold talks on the plans in Brussels next week before presenting a more detailed strategy at a summit meeting of EU leaders in December.

Von der Leyen has been pushing hard to revamp the German military, improve its procurement process and boost personnel. Last month she said Germany was ready to play a larger military role in the service of closer European defense cooperation.

(Editing by Louise Ireland)