Worksafe confirmed it issued a non-disturbance notice on April 24.
Barclay said the bank engaged the services of an asbestos management expert, who now conducts the tests and surveys before the construction company starts work on any areas of the floor. Previously, the company carried out the tests itself.
Engaging an expert "has provided an added assurance".
"Renovation work only starts when the asbestos management expert agrees it is safe to do so," Barclay said.
The non-disturbance notice was lifted on April 28.
Barclay said the team follow the correct safety procedures to assess, contain and remove asbestos from affected areas.
"Where asbestos is present we lock down the affected area until the potential risk is mitigated."
Asbestos was commonly installed in buildings as a fire retardant in the early 1970s, including the Reserve Bank building.
"This is similar to many other buildings around Wellington built in the same era," Barclay said.
"It presents no health risks unless it's disturbed and becomes airborne. Areas where asbestos is known to be present are limited to specific parts of the Reserve Bank building that are inaccessible without significant demolition of walls, ceilings or floors."
The Reserve Bank has been working with Worksafe throughout the renovation process.
Construct Wellington did not want to comment.