The DHB's smaller hospitals, at Thames, Tokoroa and Taumarunui, are generally meeting or exceeding the target.
It is the much larger Waikato Hospital in Hamilton that is having difficulty getting patients through the ED quickly enough.
"I think they have made a lot of progress," said Health Minister Tony Ryall. "The redevelopments may be having an impact on the flow of the hospital.
"I have talked to the chair [of Waikato DHB, Graeme Milne] to make sure we have got enough focus on the whole-of-hospital ED experience. He says there's a lot of work going on."
Emergency department attendances at Waikato Hospital have risen by more than 5 per cent a year since 2009.
There are hopes that a new scheme to pay general practices to treat certain patients traditionally managed in hospital, such as some with skin infections, will help control the increasing demand.
The DHB's chief operating officer, Jan Adams, said part of the ED-target problem was that Waikato Hospital wards had been extremely busy at times during the winter.
Usually it opened extra wards to take patients admitted through the ED, but this had not been possible because of construction projects. The redevelopment had also caused disruption in other ways, such as the shifting of whole departments.
The last of these changes potentially affecting ED target compliance would be completed next April, but Dr Adams hoped improvements in meeting the ED target would occur sooner.