Attorney General Maura Healey said Thursday she would agree to debate Sen. Sonia Chang-Díaz twice between the party's convention in June and the September primary, a much more limited schedule than the three pre-convention debates Chang-Díaz had been seeking.

Healey, the early front-runner in the race for governor, sent a letter to Chang-Díaz's campaign Thursday, a week after the Boston senator challenged the attorney general to three live televised debates before Democrats gather in Worcester to decide on ballot access and a possible endorsement.

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Healey campaign manager Jason Burrell said that Healey has participated in more than 70 caucuses where she engaged with voters and potential delegates to the convention since launching her campaign in January, and has also taken part in forums hosted by Progressive Democrats of Massachusetts, the SEIU State Council and the Black and Latinx Municipal Caucus.

"Media-sponsored forums and debates are important opportunities for voters to hear directly from the candidates," Burrell continued.

In addition to the two yet-to-be scheduled debates later this summer, Healey said she would take part in two more candidate forums before the June 4 convention.

The first forum has been scheduled for the evening of April 19 by Boston Ward 4 and Ward Democrats and the conversation will be moderated by GBH's Callie Crossley. The second event will be hosted by WBUR and the Environmental League of Massachusetts at 6 p.m. on April 27.

Chang-Díaz, who has trailed Healey in early fundraising and polling, hoped to have a chance to get in front of a wide swath of voters by debating Healey on television several times before the convention, where she will need to secure the support of at least 15 percent of delegates to qualify for the ballot.

She accused Healey early this week of dodging her and voters by refusing to debate before Democrats gather in Worcester. Her campaign did not immediately respond to Healey's Thursday offer.