Bavaria's state government said it and the state of Hesse filed the suit Monday with the Federal Constitutional Court. They say the system needs to be adjusted because only three of Germany's 16 states are now paying into the system while the other 13 receive payments.
Bavaria and Hesse are both run by Chancellor Angela Merkel's center-right coalition and both hold regional elections in September, when Germany also will elect a new federal Parliament. The third contributor state, opposition-run Baden-Wuerttemberg, didn't join the lawsuit.
Some 7.9 billion euros ($10.3 billion) were redistributed last year.
The system is supposed to help ensure equal living conditions nationwide.