And they claimed to be ''70 percent'' of the way towards arresting the two men on a motorcycle who slashed the 60-year-old to death on Thursday in a quiet Phuket street after failing to snatch her bag.
All of Phuket's eight police station superintendents were at Phuket City police headquarters tonight as Bangkok braid General Chatchai Potaranan took them and the media through the case so far.
The general arrived on Phuket this afternoon as the cofin containing the body of the Australian mother-of-three was being taken to Phuket airport for a flight to Bangkok and then home to Perth.
Her savage murder has triggered probably the biggest manhunt Phuket has seen, with island police and their Bangkok leaders doing everything to bring the murderous pair to justice.
Killers on the loose are not good for tourism. Right now Phuket and another favorite tourist island destination have similar problems - Phuket with the knife-wielding men on a motorcycle and Phi Phi with the unknown cause that killed Canadian Audrey Belanger, 20, and her sister, Noemi, 26, in their room at a resort a week ago.
Phuket police hope to get Mrs Smith's killers within days. Doctors have promised Phi Phi results of the sisters' autopsies on Tuesday week.
Tonight when asked by Phuketwan what was being done to more thoroughly protect tourists in the Phuket region in future, General Chatchai said he had already met with Thailand's Prime Minister Yingluck Shinawatra and deputy PM Chalerm Yubumrung, who rated the need for safety and security highly.
''It's a good start for improving safety on Phuket and making sure we don't have this kind of random act of violence again,'' he said. ''We need a good security camera system all over the island.''
Phuket is Thailand's highest tourism income earner outside Bangkok. Tourism industry leaders on Phuket are known to be concerned about the small number of police on Phuket and the danger any future serious crimes pose to tourists and income.
''We should start with Phuket and make it the 'Phuket model' for safe tourism throughout Thailand,'' he said. ''We accept that we don't have enough police, not just on Phuket but around the country.''
Detailing the murder of Michelle Smith, he said she and her friend Tammee Lynn, 42, had been out to dinner that night on the terrace at the Kata Beach Resort, one beach along from where they were staying at the Katathani Beach Resort, on Kata Noi bay.
''It was a walk of about 1.4 kilometres,'' he said. He revealed that according to one of eight security cameras in the street, the murder took place at 8.10pm - much earlier than thought.
''The notification to police did not come until 10.30pm,'' he said, leaving reporters to ponder what happened in the meantime.
[Inquiries by Phuketwan tonight show the camera's clock may be in error. Some of the women who were with Mrs Smith and Ms Lynne have said they went for a massage, after they all had dinner together, at 9pm, when Mrs Smith and Ms Lynne went shopping.
There would be no reason for the resort staff not to report the matter immediately to police.]
The murder took place in the quiet street about 200 metres from the safety of the entrance to the Katathani resort.
The meeting of the police chiefs continued tonight after the media left. At that stage, a number of photos of criminal suspects were about to be screened.