"The last place we know she was seen was at the motel. We've been there and found her belongings," he said.
"But after we know she left the motel, we just don't know where she went. She failed to check out."
It is not known what Ms Portman, who goes by the nickname Bok, was wearing when she vanished in the late afternoon or early evening.
Police have checked cellphone and bank records and there has been no sign of her since she left the motel.
Her cellphone or other belongings she may have had at the time, such as a purse, have not been found.
Mr Gutry said the unemployed woman had connections to the drug world in Auckland. It was out of character for her to go this long without speaking to her mother, he said.
"She certainly moved around a lot of different places.
"It wasn't unusual for her mother not to hear from her for a few days. But not this long."
Ms Portman drove a silver VW Passat to Auckland and Mr Gutry said the car had been recovered and examined. "We have very grave fears for her safety.
"We are working on her movements over the day that she went missing. We've done all the usual investigations and come up with nothing."
Mr Gutry said there was absolutely "no chance" she would have simply taken off.
He said anyone with information about Ms Portman's disappearance, or anyone who saw her should contact the police. "She would have been in touch with her mother.
"[Her family's] just very concerned for her and would just love for anyone to give any information which might help find her."
Ms Portman attended Rosehill College in South Auckland.
According to an online profile she had lived in Botany, East Auckland, and was self-employed for a time doing accounting for small businesses.
Can you help?If you have information about Rae Colleen Portman contact the police on 0800-723-767 (0800 Rae Portman), Crimestoppers anonymously on 0800-555-111 (0800 Crimestoppers) or visit www.face book.com/pages/Where-is-Rae-Bok-Portman.
