Christie fired the first shot on Monday, telling delegates at the Republican National Convention in Tampa that Brown was an "old retread."

Brown initially dismissed Christie's comments as name-calling and said he would take the high road. But on Thursday, in a speech to union members in Los Angeles, Brown changed tactics.

The governor said there was nothing wrong with being old since experience means he "may know a hell of a lot more than" Christie.

Then Brown challenged his East Coast counterpart to a fitness contest.

"I hereby challenge Gov. Christie to a three-mile race, a push-up contest and a chin-up contest," he said. "And whatever he wants to bet. I have no doubt of the outcome.”

Watch Gov. Brown issue the challenge on YouTube.