Sen. Scott Brown (R-Mass.) and Harvard professor Elizabeth Warren appeared Wednesday night to move toward an agreement to try to limit the presence of third-party advertising in the hotly contested Massachusetts Senate race.

Brown sent a signed pledge to Warren, the presumptive Democratic nominee, that would create a mechanism in which each candidate would pay a fee if a third-party group aired an ad in favor of him or her or against his or her opponent.

“The agreement’s terms are simple,” Brown wrote in an accompanying letter to Warren that was released to the media. “My campaign will bear a steep financial penalty if third party ads are run supporting me or opposing you, and vice-versa.”

Brown proposed that a campaign helped by a third-party ad would pay a fine of 50 percent of the cost of the advertising buy to the charity of the opposing campaign’s choice.

Warren responded late Wednesday evening in a letter of her own, saying she hoped to come to an agreement and proposed some additional clauses to expand on the pledge Brown signed.

The campaign managers of Warren and Brown will meet later this week to hash out details.

Third-party groups such as the Republican-affiliated Crossroads GPS and the Democratic-leaning League of Conservation Voters have already spent millions on ads against the candidates in the Bay State Senate race.

The back-and-forth on pushing out third-party groups began with a letter from Brown to Warren last week, asking her to renounce outside advertising.

“Rather than adopt an elitist attitude with one set of rules for yourself and another for everyone else, I urge you once again to join me in calling for an end to all spending by third party groups,” he wrote Friday.

She shot back with a letter of her own soon thereafter.

“Too often, candidates call for an end to third party influence but their words are just that, and their calls are just more empty promises and politics as usual,” Warren wrote last week. “I propose that our agreement include television, radio and online advertisements from outside groups and third parties and further, that this agreement include consequences for the campaign that fails to honor this agreement.”

It’s unclear what a final deal might look like — and whom, exactly, a moratorium on third-party ads would help the most — but the back-and-forth will continue to provide fodder for the campaign in the coming days.

Brown will officially announce his re-election campaign today at an event in Worcester, Mass. It’s the two-year anniversary of his upset victory over state Attorney General Martha Coakley (D). In a bit of counter-programming, Warren will hold an online “money bomb” today, an attempt to raise big bucks in 24 hours over the Internet.