As an American citizen you are required to file taxes, even if you are earning money in another country. The US is, I believe, the only Western country that has this law. It applies to earned income and there is an exclusion where you don't have to pay any US taxes if you earn less than $80,000 ish. It sounds a lot but depending on the exhange rate and where you are (London for me and it was about £45,000 because of the exchange rate last year) it could be a barely slightly higher than average wage.
So that's the US side of things! For the Israel side of things, I imagine it depends on why you are over there and what type of visa you have. Is there a visa forum on the internet anywhere? I imagine they can help with the rules and laws.