A Samoan police constable familiar with the case told the Herald the investigation into the 24-year-old's disappearance was ongoing.
Police on the island are also being assisted by the New Zealand High Commission in Apia, and the Navy will send a family liaison officer to Samoa within the next 48 hours.
Tua's parents and two older sisters have also flown to Samoa to help with the search.
Tua is described as an "adventurous boy that loves travelling and explore unique places". Photo / Supplied
Tua's Auckland-based aunt, Faye Tua, told the Herald her nephew was due to return to Auckland on Monday night, and was expected to be back at Devonport on Tuesday.
"We first got the call that he was missing on Sunday afternoon. The police contacted the family in Samoa.
"We haven't heard from him since Saturday. He borrowed a car just to go sightseeing. The first place that he stopped, that's the first place that he went missing."
Tua was last seen at To-Sua Ocean Trench, a popular tourist and swimming spot on the southern coast of Upolu Island.
"People who were at the trench called police and said his car was still parked at the carpark - there's no sign of him," Faye Tua said.
She said her brother and Tua's father, Lemafoe Tua, was "very upset" to learn his child was missing.
"We stayed with [Lemafoe] all Sunday, and then we got a call from one of the family who lives in Samoa who said 'the search had been called off for the night'.
"All we've been doing is waiting for news, but my brother and his wife flew out to Samoa on Monday to help look for him."
The To-Sua Ocean Trench was the last place Joseph Tua was seen. Photo / Ben Mikha
She said the family was "frustrated" to find no signs to explain Tua's disappearance.
"The last time he went [to Samoa] was when he was very young, this is the first time he's been back to Samoa as an adult.
"This is the kind of thing you watch on the news and [we] never thought in a million years that it will happen to our family."
