Officers responded to reports of a robbery at a Wells Fargo at A and 18th streets in Antioch around 11:10 a.m., Kelley said.
Three male suspects had allegedly robbed the bank before fleeing the scene, according to Kelley.
Police from multiple agencies pursued the suspects to Pittsburg, where two suspects were subsequently shot, Kelley said.
Kelley did not know who shot the suspects or what their conditions were.
No officers were injured, Kelley said.
There were customers inside the bank when it was robbed, but no injuries were reported from the robbery, Kelley said.