My Israeli identity card makes no mention of my religion (I have none) but under 'Nationality' ('Le'um') it says 'Jewish'. So yes, there is such a thing as Jewish nationality in Israel, and one need not be religiously Jewish to be Israeli.
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One killed, three wounded in stabbing at asylum center in Sweden (AP)
from the article: Israeli author Yoram Kaniuk asks court to cancel his 'Jewish' status