Speaking after meeting Sinn Fein on Wednesday, DUP leader Arlene Foster said more meetings were planned.
"The dialogue continues in a very good nature, I think that's positive and obviously the focus is on getting devolution up and running again and as quickly as possible," she said.
"My team has met Sinn Fein on legacy issues today and we have been talking about the Stormont House Agreement, we have been talking about all the issues that have concerned us, including the issues around soldiers and how they are treated, how members of the security forces are treated, dealing with issues about the past."
Sinn Fein broke off its meeting with Mr Brokenshire on Tuesday and said all he did was "waffle, waffle, and more waffle".
Mrs Foster said that waffle was a very pejorative term to use, adding that the DUP had had "very good engagement" with Mr Brokenshire.