The prayer for the government is a biblical prayer, and is read during the Saturday morning service on Shabbat. The concept of praying for the wellbeing of the government was started in 586 B.C.E. by the prophet Jeremiah after the first expulsion from Jerusalem. Seeing as the Jewish people could not govern themselves, they implored God to guide their foreign rulers. David Abudarham first introduced this prayer into the modern siddurim (prayer book) in the 14th century. Jews have adopted different prayers for the governments of the countries in which they live. The prayer is read aloud after the Torah reading, but before the Torah is placed back into the ark. This blessing asks God to guard the proceedings of the government and the nation’s leaders.
http://www.jewishvirtuallibrary.org/jsource/Judaism/govprayer.html
Sources: Eisenberg, Ronald L. The JPS Guide to Jewish Traditions. PA: Jewish Publication Society, 2004; "Praying the Welfare of the State of Israel"
Avinu Shebashamayim
God in heaven, Rock and Redeemer of Israel,
bless the State of Israel,
the first flowering of our redemption.
Shield it with Your love, spread over it Your canopy of peace;
provide light and truth to its leaders,
and direct them with Your good counsel.
Strengthen the hands of those who defend our Holy land,
deliver them and crown their efforts with triumph.
Bless our land with peace, O God,
and its inhabitants with lasting joy, and let us say, Amen.
Avinu Shebashamayim tzur yisrael v'goalo
bareich et m'dinat Yisrael reishit tzmi'chat g'ulateinu.
Hagein aleha b'evrat chasdecha
ufros aleha sukkat sh'lomecha;
ush'lach orcha vaamitcha l'rosheha sareha v'yoatzeha,
v'takneim b'eitza tova milfanecha.
Chazeik et y'dei m'ginei eretz kadsheinu,
v'hanchileim Eloheinu y'shuah, v'ateret nitzchon t'atreim;