He wrote: “The political and economic turmoil the UK is currently experiencing shows this clearly.
“And it also shows that the very people who screamed ‘leave’, who shouted ‘down with the EU’, have no answer to the question ‘what next?’ when the country leaves or the EU is abolished.
“That is not only foolish and irresponsible, it is also playing with fire.”
He attacked those seeking to “instrumentalise” national sentiment, citing former French President François Mitterand who said “nationalism means war”.
Mr Steinmeier said he and French Foreign Minister Jean-Marc Ayrault had set out ideas in the wake of the Brexit vote that focused on “making Europe better”.
The statement the pair produced called for a new EU “fiscal capacity”, “a permanent civil-military chain of command”, the “harmonisation of criminal law” and an “integrated European asylum, refugee and migration policy”.