"We love him very much and there is nothing he has done that he should ever feel ashamed of.
"We have always been very proud of him."
His family are asking anyone with information to urgently contact them or police, she said.
Seaside Park in Ōtāhuhu, an area he liked to visit, has been checked with a wide-ranging search effort also including the suburbs of Mt Richmond and Mt Wellington.
"Sometimes he goes for very, very long walks. He has been known to have even walked from here to St Heliers."
However, his whereabouts since that early hour of April 20 remain unknown and area inquiries by police yesterday involving search and rescue staff have failed to find him.
Further inquiries are being made by police this morning in the Ōtāhuhu area.
Stephen is of Indian ethnicity and of slim-build.
His dog Ziggy is a tan-coloured Staffordshire-cross breed, with a white chest and paws.
Anyone with information is asked to contact Counties Manukau Police by phoning 105, quoting file number 200420/6609. You can also contact Crimestoppers anonymously on 0800 555 111.