"Please accept my apologies on behalf of Immigration NZ for the stress and inconvenience this has caused you and the Johnston family."
The incident was widely reported in Australia and Britain and Prime Minister John Key described Immigration's treatment of Ms Pache as "heavy-handed".
Ms Pache said she "would have assumed" Immigration had more important issues to deal with "than myself going on holiday with ... no intentions to stay, and not stealing any work [from] people there".
On her arrival at Queenstown Airport in December, Ms Pache told an immigration official she might babysit during the week-long holiday in Wanaka. She was not expecting to be paid but her employers had paid her airfares and accommodation.
She spent a night in a cell before being deported to Australia, and was described by her employer Dr Johnston as having been "terrified".
Ms Pache said the apology had helped her get over the incident. "I hope other nannies will be careful now. I am still angry about this officer, that pushed me out of this beautiful New Zealand because I was being honest. Maybe he likes the liars."
Ms Jehle also told Ms Pache Immigration was reviewing its border operations "settings and responses", including custodial arrangements for people refused entry at airports where it had no accommodation for people waiting for their return flight.
Dr Johnston has laid a complaint with the Independent Police Authority. ODT