According to Article III, Section 2 of the U.S. Constitution, the U.S. Supreme Court has the power to resolve disputes between states. This authority is considered original and exclusive jurisdiction for the Supreme Court.
There are several areas that the Constitution considers original jurisdiction for the Supreme Court: legal actions between states and the federal government, states and citizens of other states or aliens, and those involving foreign dignitaries, in addition to interstate controversies. Only the power to settle disputes between states is exclusive to the Supreme Court, however. The Supreme Court largely acts as an appellate court, or one that reviews cases that were already tried by lower level courts with original jurisdiction, and rarely needs to exercise its original jurisdiction duties. Most disagreements between states concern claims to property.