Well, it's good to know that the Japanese really do have a plan for dealing with aliens and Godzilla. Giant monsters and zombies are two subjects that have spawned more elaborate planning from myself and my friends than almost anything else, and it's good, in kind of a sad way, to know that foreign heads of government have similar concerns.
FYI, the reason there's any question at all as to whether or not the Japanese could preemptively fire upon Godzilla is the good ol' postwar MacArthur Constitution, which abolished Japan's military and replaced it with a "self-defense force". (That's why when you watch Godzilla movies all the tanks say JSDF on them.) War is, in all seriousness, unconstitutional in Japan, and the country is prohibited from taking aggressive action on the battlefield. Even Japanese forces deployed in foreign lands as part of UN peacekeeping groups can only fight to protect themselves, allied forces, civilians, and Red Cross personnel. However, this could be circumvented in the case of Godzilla by declaring him to be a "natural disaster", as Minister of Defense Shigeru Ishida explained to, I assume, a dumbstruck crowd of journalists over the weekend. If Godzilla were, to borrow a phrase, classified as an "enemy combatant", it would technically be illegal for the Japanese to attack him should he be, for example, simply hanging offshore near the nation's coastline but not actually attempting to come ashore or eat ships full of Red Cross volunteers.
There's actually been some talk in the Japanese Parliament lately about getting rid of the JSDF and replacing it with a proper army, mostly in response to concerns about North Koreas's nuclear ambitions. It remains to be seen if the Japanese have a contingency plan prepared in case Godzilla should attack the Korean Peninsula in search of radioactive fuel to power his nuclear metabolism.