Police have arrested two suspects over the murder of an Australian travel agent and the wounding of her travelling companion in a street in Phuket on Wednesday night.

Michelle Smith (Photo from Facebook)

Phuket governor Tri Augkaradacha said on Monday that both men were in custody in Chumphon.

They were expected to be returned to the resort island later Monday, Mr Tri said.

Phuket deputy police chief Pirayoot Karajedi identified the suspects as Surasak Suwannachote, 26, from Nakhon Si Thammarat, and Surin Thapthong, 36, from Ratchaburi.

Mr Surasak, who is accused of fatally stabbing Australian Michelle Smith, 60, during a bag snatch, had been hiding in Nakhon Si Thammarat. Mr Surin, the motorcycle driver, had been hiding in Samut Songkhram, Pol Col Pirayoot said.

Officials and representatives from the tourism industry met in Phuket this morning to discuss tourist safety in the wake of the Smith murder and other increasingly frequent attacks on foreign tourists.

Last Wednesday, Smith, part of a group of travel agents from Perth visiting the area, and her friend Tammee Lynn, were walking back to their hotel in Karon around 10.30pm after eating at a restaurant. They were attacked by two bag snatchers on a motorcycle.

As Smith struggled to hold on to her bag, one of the men stabbed her in the chest. The two women walked off and then Smith collapsed a short distance away and died at the scene. The motorcycle thugs fled empty handed.

WARNING: GRAPHIC CONTENT - A video clip, uploaded to YouTube by thePhuketNews1, shows video  footage of two men attempting to steal Smith's handbag.