The suspect, who comes from the Phang Nga province north of Phuket, was spotted by a witness on Mai Khao Beach close to where the body of Hanna Charlotta Bäcklund was found.
“Police have a witness who saw him leave there at the time in question,” Christina Palm from the Swedish Consulate told the TT news agency.
Seven police districts are participating in the search for the suspect.
Bäcklund’s 29-year-old travelling companion was taken in for renewed questioning on Monday. She also received a visit from Thailand’s Minister for Tourism Weerasak Kowsurat, who travelled to Phuket in a bid to speed up the investigation.
“He passed on his condolences,” said Christina Palm.
The 29-year-old was planning to Sweden as soon as possible having spent the weekend in hospital receiving treatment for shock.
Bäcklund was found dead after taking a walk on the beach on Saturday morning. She had been staying with her friend in a tent on a stretch of beach that was relatively quiet and undeveloped.