Mr Savaki was not an illegal immigrant who had been trying to evade detection; he was a high-profile person in a high-profile sport, Mr Clark said.
He remained in the country after being selected for the Poverty Bay rugby team and had not come to further official notice until recently charged with drink-driving.
Crown prosecutor Kim Laurenson sought a warrant to detain Savaki until deportation but agreed to have the application adjourned for a fortnight to allow him to leave voluntarily.
He was remanded on bail with conditions including reporting to police three times a week.
Poverty Bay coach Mutu Ngarimu said he had no idea until yesterday that lock forward Savaki was an overstayer.
"As for the drink-driving, that's not what we expect from players representing Poverty Bay.
"It's totally against team protocol and what we are trying to achieve, on and off the field - players proud to wear the jersey and respecting that it is an honour that not every rugby player gets.''