May I travel with my father's ashes into Israel?

This is probably a not very common request, and I couldn't find information about it online (I did find information for transferring a body for burial in Israel, but this is not the case here).

On the Israeli tax authority site, there is a list of forbidden items, and items that need a special approval. Human ahses are not on that list. (An English translation of the list can be seen here).

But, because of the sensitive nature of the item, and assuming that you probably don't want any chances of your father's ashes being confiscated, or even worse, discarded, I would recommend contacting your local Israeli consulate to inquire and make the proper arrangements, if necessary.

One more thing, cremation is very unpopular in Israel, so there is only one company that offers the service, Aley Shalechet¹. And according to their site, they do perform ashes scattering services for people from abroad, so you might want to contact them and ask them; you probably have a better chance of getting a responce from them than from the Israeli tax authorities.

^{1 - I am not afiliated with the company in any way.}