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Leaflet is a dynamic, client-side mapping framework, so no: you can't create static maps with it...
You have to use a web service like that from Google, Bing, MapQuest or similar ones.
Actually my first answer isn't completely true: you could create your own web service using something like PhantomJS and Leaflet running on a web server. This requires quite some knowledge and a dedicated web server where you can install your own software.