Senator Scott Brown said he will accept a debate at the Edward M. Kennedy Institute but only on the condition that Vicki Kennedy stay neutral in the election and that MSNBC not be included as a broadcast partner.

The Brown campaign said in a press release that it would agree to allow former NBC anchor Tom Brokaw to moderate.

Elizabeth Warren has already accepted the Sept. 27 debate, but Brown had previously not committed. The candidates are jointly committed to two other televised debates so far, one in the Boston market and a second one in Western Massachusetts.

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Vicki Kennedy, Senator Kennedy’s widow, had proposed a third debate. But she has been an active Democrat, causing some to question whether Brown should accept the invitation. And MSNBC, home to many liberal talk show hosts, had been mentioned as a potential broadcast partner.

The Edward M. Kennedy Institute for the United States Senate would not say Monday whether Vicki Kennedy would refrain from endorsing or campaigning for Brown or Warren. In a statement Monday night, the Institute said it looked forward to “discussing the terms of the debate in person with the Brown campaign and the Warren campaign.”

Following that statement, the Brown campaign said it would negotiate logistical details after its conditions are met.

In a letter to the Institute Monday, Brown’s campaign manager Jim Barnett wrote: “In order to proceed, we need to know that in keeping with the spirit of neutrality expressed in Vicki Kennedy’s letter that she will not endorse or otherwise get involved in this race.

“Furthermore, while we accept Tom Brokaw as a moderator, we prefer debates with local media sponsors, not out-of-state cable networks with a reputation for political advocacy.”

Though his letter advocates the involvement of local television, Brown has not yet responded to a request by a consortium of Boston media outlets, including television stations and the Boston Globe, to participate in a third televised debate.

In an e-mail Monday, Brown’s campaign spokeswoman, Alleigh Marre, said if the conditions are met for the Kennedy Institute debate, the campaign would be open to sponsorship by the Boston consortium.

Brown has agreed to two radio debates, including one moderated by Dan Rea, a conservative-leaning talk show host, and another hosted by Margery Eagan, a Boston Herald columnist, and Jim Braude, a Democrat and former Cambridge city councilor. Warren has agreed to the consortium debate but not the radio debates, saying she wants to reach a larger audience through television.

In a statement Monday, MSNBC said it had not signed any agreement to broadcast the debate, nor been approached.

Vicki Kennedy’s original invitation to the campaigns last week said that Brokaw had agreed to moderate the debate, and “we expect that the debate would therefore be carried on our local NBC affiliate and/or MSNBC.”