His return to New Zealand followed the publication of a story in The Daily Telegraph this morning which alleged the married All Black had a relationship with a former Australian model.
NZR said it could not comment on the Kaino allegations or further details about Aaron Smith's personal life which were published today as both were "personal matters".
But NZR said it felt for all of those affected.
Chief Executive Steve Tew said the NZR understood that the game and players were under public scrutiny and these latest stories in the media were concerning.
"As an employer, we will take some time to assess this. While NZR does not wish to comment on individual behaviour, it is clear that this is really hurting rugby, all the people concerned, our fans and supporters."
"We take these issues very seriously, and are also mindful that these issues affect people with families and loved ones," he said.
NZR was grappling with its cultural reputation, Mr Tew said, and the Respect and Responsibility Review which was currently under way was even more important.
The review would be presented to the NZR Board in August and would be made public sometime in September.