He told police he knew about the crime but didn't kill Peter Reisz. Police say Mr Kvalka surrendered himself to the Samui Tourist Police yesterday, after a search began for him in relation to the murder of fellow Hungarian Mr Reisz.
Mr Kvalka has now been transferred to the Thung Thong Police Station in Phuket while the investigation continues.
Mr Kvalka is one of two suspects in the murder case. Police say the other man, Hungarian/Israeli national Moshe David, confessed to the murder of Mr Reisz on Thursday, after being tracked to Bangkok through the use of his ATM card.
Arrested in the capital, he was brought back to Phuket and on Friday re-enacted the events at the crime scene.
The body of Mr Reisz was found last Friday (November 30) in Patong. He had been stabbed multiple times and bashed in the head, then dumped, wrapped in plastic. The police believe he was murdered on November 24.