"Joao Felipe is a strong boy, brave, playful and full of life. He always lived it intensely."
Mrs Melo said she believed her son was "somewhere and that he will soon be found well and counting this adventure".
She planned to wait up all night for news and to pray, while other family members travelled to New Zealand.
But in New Plymouth, Inspector Frank Grant had no hope to offer the families.
He said the focus of the rescue effort had switched to a body-recovery mission.
The two boys and instructor Bryce Jourdain, 42, have been missing since they plunged into the stormy sea off Paritutu Rock in New Plymouth on Wednesday afternoon.
The boys were part of a group of mainly international students from Spotswood College making a rock climb on Paritutu, the 150m landmark that overlooks Port Taranaki.
It's believed the boys fell into the water and Mr Jourdain leapt in to rescue them.
The course was being run by the Taranaki Outdoor Pursuits and Education Centre (TOpec), which yesterday faced criticism from some students and parents for taking the group out when the weather was poor and the sea swells were up to 3m.
TOpec chairman David Grigg promised full co-operation with investigators.
He said statements were expected to be taken from TOpec staff and the surviving students, who were lifted from the rock by rescue helicopters.
"I appreciate people still have a lot of questions about what occurred.
"We have an investigation under way that will run alongside a Labour Department investigation."
Spotswood College board of trustees chairman Ross Dingle said an investigation would be held, but the school's immediate focus was on supporting its students and the families of the missing.
Counselling has been offered to classmates of Stephen and Felipe, many of whom took advantage of a scheduled lesson-free day to wait at Paritutu for news.
One of the many who braved the cold was River Price, a former Spotswood College student.
She said she spoke to Felipe last week and he had told her how happy he was to still be in New Zealand.
"He said he decided to stay another three months to enjoy New Zealand more."
Felipe liked to sing and had the voice "of an angel", Ms Price said.
His host family yesterday joined the beachside vigil.
"His host brother is here, his family, they aren't good," said Ms Price. "It's pretty bad, it's tragic, just awful."
She had seen some of the international students who were on the trip and said they were so traumatised they could hardly speak.
"The look on their faces was just ... I gave them a hug. There was nothing we could do. They told me to watch the news when I got home. They said they'd fallen in."
She could not understand why the students had been on the trip.
"It was horrible out there. Whoever told them to go out there was wrong."
A Spotswood College parent, who asked not to be named, said hard questions needed to be asked of TOpec and a full review done to prevent another tragedy.
The search for the trio was to resume early today. It was hoped police divers would be able to join the search after being unable to enter the water yesterday because of rough conditions.
Prime Minister John Key said a full coroner's inquiry would be held.
"We need to understand if there's been any errors ... and we'll get to the bottom of that.
"Any kind of physical activity like this comes with a degree of risk. But obviously we make sure, when youngsters are involved, that that's a very managed risk.
"If something's gone terribly wrong, which in this case it has, we need to find out why and if there's things that need to change, then they will be changed."
