I’m not sure why, but when you first make aliyah the government will only issue you a "teudat ma’avar" or "travel document in lieu of passport." You have to use it when you enter or leave Israel, but when you enter or leave other countries it may or may not be accepted, so you have to have another passport with you. After having lived in the country for one year, you are eligible for a regular passport.
It’s kind of funny the conflicting messages you get from different parts of the Israeli bureaucracy. A few weeks ago when I was coming back from a trip to London, the security person looked at my teudat ma’avar and asked "why don’t you have a regular passport yet?" I explained I was told the teudat ma’avar is good for several years, etc., etc. But the question inspired me to go ahead and get the real passport. Another advantage of the real passport is you can sign up for the biometric identification fast line when you come back to Israel, which spares you standing in line.
But when I went to Misrad Hapanim (the Interior Ministry) to get the passport, the clerk asked "why do you want a passport? You can still use the teudat ma’avar." I explained I travel a lot, and wanted to be able to use the biometric line. Then when she looked me up in the computer she had to call a supervisor because I’ve travelled so much in the last 18 months since we arrived she wasn’t sure I had the one year actually in the country. After a few minutes they were able to figure out that I met the requirements and they accepted the application.
This is one of the few areas where Israel is much faster than the US. In the US it can take a couple of months to get a passport. Here in Israel I received the new passport in about three days.
Of course, I remain an American citizen and still have my US passport. So when I travel, I can use the passport that gives me the best deal on visa fees. Last year I discovered, for example, that it’s cheaper to travel to India on an Israeli passport than on an American one — since the US raised visa fees to $135, the Indian government has reciprocated for Americans; but for Israelis the fee is much less.