公使は、大使に次ぐ役職で、Ministerが使われます。

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Note added at 16 mins (2010-06-24 18:35:19 GMT)
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この場合、米国に駐在する日本国公使なら、Minister of Japan to the United States of Americaとなります。
日本国に駐在する米国公使は、United States Minister to Japanです。

- (Japan’s) Minister for U.S.-Japan relations or Minister for U.S.-Japan relations

- "Japan-US relations" is also used but since it says “米国公使” I suggest having "U.S." in front.

- Ms. Kawaguchi was Japan’s Foreign Minister (or: Minister of Foreign Affairs) but since that term is not used in your document and, instead, it uses “米国公使”, I would say that (Japan’s) Minister for U.S.-Japan relations would fit well. Especially since Ms. Kawaguchi was involved in U.S.-Japan relations.

- Ms. Kawaguchi Japanese by nationality, so she is a Japanese Minister or “Japan’s Minister” and not a “United States Minister.”

- In searching Yawaguchi-shi’s biographies, one can see that she was Japan’s Environment Minister and Japan’s Foreign Minister. (Please see first website below)

- Miho Ohashi’s answer is “Minister at the Embassy of Japan in the United States.” Although this is a position, I believe this is a different situation from Ms. Kawaguchi’s since his (Mr. Ihara’s) is like that of an ambassador who lives in the country to which he is assigned. So this Mr. Ihara lived in the United States from (2004-2006) as Minister at the Embassy in the United States.

http://www.icnnd.org/releases/090215_js_evans_kawaguchi.html
Yoriko Kawaguchi (Japan) (Co-Chair)
Ms Kawaguchi was a MITI Director-General, Managing Director of Suntory Ltd, and then Japan’s Environment Minister from 2000 to 2002, and Foreign Minister from 2002 to 2004. She is currently a member of the House of Councillors and Chair of the Liberal Democratic Party Research Commission on Environment.
http://www.presstv.ir/detail.aspx?id=128099§ionid=351020...
Japan minister fired over US airbase
Japan's Prime Minister Yukio Hatoyama dismissed consumer affairs minister, Mizuho Fukushima, The Wall Street Journal reported on Friday.

http://www.acronym.org.uk/dd/dd88/88news03.htm
Yoriko Kawaguchi (Japan) (Co-Chair)
Ms Kawaguchi was a MITI Director-General, Managing Director of Suntory Ltd, and then Japan's Environment Minister from 2000 to 2002, and Foreign Minister from 2002 to 2004.

http://www.mofa.go.jp/region/n-america/us/fmv0309/unstate.ht...
STATEMENT BY
H.E. MS. YORIKO KAWAGUCHI
MINISTER FOR FOREIGN AFFAIRS OF JAPAN
http://www.unu.edu/globalization/2007/bio.html
Yoriko Kawaguchi
Member of the House of Councillors, Japan (former Minister of Environment and Minister of Foreign Affairs of Japan)
Yoriko Kawaguchi is a Member of the House of Councillors, Japan. She was formerly Minister for the Environment (2000) and Minister for Foreign Affairs (2002). She has served as Director-General, Global Environmental Affairs, Ministry of International Trade and Industry, as a Managing Director, Suntory Ltd., and as Special Advisor to the Prime Minister of Japan, responsible for foreign affairs. She serves on the jury of the Zayed International Prize for the Environment (UNEP) and is Chair of the Asia-Pacific Forum for Environment and Development (APFED)2. She is a member of the Foundation Board of the Forum of Young Global Leaders, World Economic Forum, the President's Council on International Activities, Yale University, and of the Club of Madrid/UN Foundation High Level Task Force on Climate Change. She holds a B.A. in International Relations from the University of Tokyo and a M.Phil. in Economics from Yale University (U.S.).
http://www.yale.edu/japanus/japan_at_yale.htm
Project on Japan - U.S. Relations
Yale University’s connections with Japan go back to the 19th century. Yale graduates traveled to Japan soon after the Meiji Restoration of 1868 and contributed to the country’s modernization. Dwight Whitney Learned (C 1873, G 1875) was one of the first teachers at Doshisha University and stayed in Japan for over 50 years, translating books of the Bible into Japanese and introducing the study of political economy. Well-known Japanese such as Okubo Toshitake studied at Yale in the 19th and early 20th centuries. This tradition continues, with current Foreign Minister Yoriko Kawaguchi and Ambassador to the United States Ryozo Kato both having taken degrees at Yale.

"envoy" is generally used to designate a foreign agent second in rank to a minister/secretary or ambassador. i realize from reading the other answers that the discussion is nearly closed, but thought i'd posit that possibility for added nuane/clarity.