The Judiciary Act  (Section 13)
The act to establish the judicial courts of the United States authorizes the Supreme Court "to issue writs of mandamus, in cases warranted by the principles and usages of law, to any courts appointed, or persons holding office, under the authority of the United States." 
Article III of Constitution, Section. 2 
The judicial Power shall extend to all Cases, in Law and Equity, arising under this Constitution, the Laws of the United States, and Treaties made, or which shall be made, under their Authority;--to all Cases affecting Ambassadors, other public Ministers and Consuls; --to all Cases of admiralty and maritime Jurisdiction;--to  Controversies to which the United States shall be a Party;--to Controversies between two or more States;-- between a State and Citizens of another State;--between Citizens of different States; --between Citizens of the same State claiming Lands under Grants of different States, and between a State, or the Citizens thereof, and foreign States, Citizens or Subjects. 

In all Cases affecting Ambassadors, other public Ministers and Consuls, and those in which a State shall be Party, the supreme Court shall have original Jurisdiction. In all the other Cases before mentioned, the Supreme Court shall have appellate Jurisdiction, both as to Law and Fact, with such Exceptions, and under such Regulations as the Congress shall make. 

Exploring Constitutional Conflicts