A google for "japan government official website" turns up http://japan.kantei.go.jp. We can then use the ipinfo.io API to find out which network this is on:

  $ curl ipinfo.io/`dig +short japan.kantei.go.jp`
  {
    "ip": "202.32.211.142",
    "hostname": "No Hostname",
    "city": null,
    "region": null,
    "country": "JP",
    "loc": "35.6900,139.6900",
    "org": "AS2497 Internet Initiative Japan Inc."
  }

We can lookup more details at http://ipinfo.io/AS2497. It looks like lots of different organization share this network, including Coca-Cola, and a bunch of universities, so filtering based on this network is going to get us what we're after. You can also go to http://ipinfo.io/countries/jp and see all of the networks in Japan. There are a few that are government related, but there doesn't seem to be a main or single network that the government uses.

Things are easier in the UK where you have http://ipinfo.io/AS29214 (Houses of Parliament) or Ireland where you have http://ipinfo.io/AS15806 (Irish Government)

Why do you assume the website and their internet connections are in the same block?

Many companies and organisations use external hosting.

You just have to know. :)

Try asking someone in the Japanese Open Knowledge chapter: http://okfn.jp.