"We are sorry for the inconvenience but tenant safety is our priority."
Problems with the Gordon Wilson complex were first uncovered in 2010, when HNZ saw work was needed to remove loose concrete.
It was also found the complex needed significant maintenance work.
Engineers said structural inspections would have to be carried out every 12 to 24 months.
Mr Bignell one of those inspections identified the latest problem.
"We are confident that the issues relating to this complex are isolated to this complex only."
Housing New Zealand said it would be working with tenants to support them during the rehousing process.
It would cover "all reasonable" rehousing costs, Mr Bignell said.
"We appreciate that this maybe an unsettling time for our tenants but we want to reassure them that we are doing everything we can to find an alternative state rental property that will meet their needs."
Labour's deputy leader, Wellington Central MP Grant Robertson, said he would meet Housing New Zealand officials tomorrow to seek an assurance all the tenants in the block would be accommodated in suitable, local accommodation.
"The safety of residents is paramount, and Housing New Zealand is right to move swiftly if they have identified a serious problem. But they must recognise that many of the residents are vulnerable elderly people."
"Seven days is a very short period of time for someone to move from their home. If they are to be relocated, it must be as close to the flats as possible. They have doctors, caregivers and other services nearby which provide them with essential services. This link needs to be maintained,'' he said in a statement.
HNZ vacated 18 tenants from flats neighbouring the Gordon Wilson complex in 2011.
It said emptying the McLeans flats complex at 314 The Terrace was necessary as the building was earthquake prone and needed upgrades to meet modern building standards.
