Paulette Kaleikini and her family, designated as cultural descendants of any remains found at the site, has been trying to stop the project, alleging that the state Department of Land and Natural Resources, the O'ahu Island Burial Council and developer General Growth Properties acted improperly by having, or allowing, approximately 35 sets of remains to be removed and housed in an air-conditioned trailer nearby on the construction site.

Circuit Judge Glenn Kim said he believed any remains found are being kept in a safe place and that he did not believe there would be irreparable harm done to them. He also said he did not believe it likely that the Kaleikinis would prevail on the merits of the case.

Being built on the six-acre site are a Whole Foods store, other retail space and a residential tower at a cost of $150 million.

General Growth vice president Jan Yokota said the company is sensitive to the situation and will continue to work with Kaleikini's family.