Ms. Warren promptly agreed, calling Mr. Brown within hours of receiving the letter to discuss how to draw up “an enforceable agreement.”

Seeking the upper hand on the issue once again, on Wednesday Mr. Brown proposed that whenever an outside group runs an ad, the candidate it benefits should donate half the cost of the ad to a charity of his or her opponent’s choice. Ms. Warren responded that they should “go beyond” that proposal and suggested others. Aides to both candidates are scheduled to meet Friday on the matter.

Mr. Brown is hoping that the everyman appeal he cultivated two years ago as a pickup-driving candidate with a zest for Boston sports teams will remain a potent tool against an opponent who comes from academia, and whom he pointedly refers to as Professor Warren. It seemed to work for him on Tuesday as he visited a hardware company in Westminster and chatted with its employees about the New England Patriots, the Boston Bruins and his workout regimen.

Mr. Brown was not driving his famous pickup truck, but he mentioned it (“It’s got 220,000 miles on it now, runs well”) and wore the barn jacket that was his much-photographed campaign uniform in 2010.

“He seems like a regular guy,” said Mike Girouard, an assistant manager in the company’s warehouse, who said Mr. Brown had his vote. “He hits all the points of someone who’s middle class.”

Seeking to define Ms. Warren for voters before she does so herself, Mr. Brown frequently describes her as “a self-proclaimed rock thrower” who “wants to leave blood and teeth in the streets.”

The latter reference is to a comment Ms. Warren once made while fighting for the Consumer Financial Protection Bureau — that if Congress failed to give the agency significant powers, her preferred alternative would be “no agency at all and plenty of blood and teeth left on the floor.”