"I would suggest they take the opportunity to return to resolve this matter before the outstanding sum is spent."
Gao and Hurring fled Rotorua with $3.8 million three weeks ago after Westpac put $10 million into Gao's account.
The bank was able to recover the remaining amount, but the couple are believed to be hiding in Hong Kong.
Law professor Warren Brookbanks, of Auckland University, said last night that drafting criminal charges could be difficult.
Because the bank had, in effect, handed over the money, albeit by mistake, "it can't be pursued as a simple case of theft".
And to prove fraud usually required an element of false pretence or false representation, and no evidence of those had been reported.
Mr Harvey also said yesterday that police were preparing a formal request to the Chinese Government for assistance.
"The fact we are taking this step shows how seriously we are taking this investigation."
New Zealand has a mutual assistance treaty with China and Hong Kong under which police can apply for help on criminal matters.
Police also confirmed the identities of the runaways as 29-year-old Leo Gao and 30-year-old Kara Mary Jo Hurring (also known by the surname Yang) and said a family member who had been travelling with them had returned to New Zealand.
Mr Harvey would not name the person, but at lunchtime yesterday Aroha Hurring - sister of Kara - arrived at Auckland Airport, where she was met by a team of detectives.
It is understood she left New Zealand to join Gao, her sister and her 7-year-old niece days after their sudden departure.
Yesterday a man who answered the phone at the home of Kara's father, Chris Hurring, said they had not heard from Aroha or Kara.
Linda Woon, principal at Otonga Primary School where Leena is enrolled, said Hurring phoned the school to extend the family "holiday" some time ago.
Leena did not return to school after the term 2 break, she said, and then her mother phoned to extend the break further.
"I just received a phone call to say 'We are not going to be back when we thought'."
Ms Woon said the school did not connect the child's absence and the multi-million-dollar runaways until a private investigator paid a visit.
Twenty-two-year-old Aroha Hurring charted the fugitives' progress to Hong Kong, Macau and into mainland China on her Facebook page, which has been deactivated.
An official at the Chinese Embassy in Wellington,said no letter had been received from New Zealand police.
