In March 1876, Hunt was appointed Attorney-General of Louisiana, and in July of that year he was the Republican candidate for this office. Both parties claimed victory in the election, but Hunt lost the position when President Hayes recognized the Democratic government of the State. As compensation, the President appointed him Associate Judge of the United States Court of Claims, 15 May 1878. He served in this capacity until he became President Garfield’s Secretary of the Navy.
Secretary Hunt rendered invaluable service by reporting that the Navy, grossly neglected after the Civil War, was no longer able to protect Americans abroad. He appointed the first Naval Advisory Board which undertook the work of rebuilding the Navy, emasculated by public apathy and lock of funds. After Vice President Arthur succeeded Garfield in the presidency, he retired Hunt from the cabinet by appointing him Minister to Russia 7 April 1882. He died February 1884, while representing the United States at Saint Petersburg.