Debra Robinson delivered a tribute to her sons at a beach in San Diego on Tuesday.
“Our hearts are broken and the world has become a darker place for us,” she said. “They were young men enjoying their passion of surfing together.
“Jake’s passion was surfing, and it was no coincidence that many of the hospitals that he worked in were close to surfing beaches.”
“Live bigger, shine brighter, and love harder in their memory,” she said, and thanked Australian officials and supporters there and in the United States.
Mrs Robinson, who also paid tribute to Jack Carter Rhoad, said her sons’ bodies, or their ashes, will eventually be taken back to Australia.
“Now it’s time to bring them home to families and friends,” she said. “And the ocean waits in Australia.”
Prosecutors have identified three people as potential suspects, two of whom were caught with methamphetamines. One of them, a woman, had one of the victims’ mobile phones when she was caught, they said.
Prosecutors said the two were being held pending drug charges but continue to be suspects in the killings.
A third man was arrested on charges of a crime equivalent to kidnapping, but that was before the bodies were found. It was unclear when or if he might face more charges.
The third man was believed to have directly participated in the killings, prosecutors said.
33-year-old Callum, Jake, 30, and their friend Jack, also 30, had posted photos on social media of isolated beaches shortly before they went missing.
Callum had reportedly been living in the US to try to become a professional lacrosse player, while Jake, a doctor, had flown out to visit him two weeks ago.
Thieves likely saw their truck and tents and wanted their tyres but the men probably resisted, said prosecutor Maria Elena Andrade Ramírez.
She said the bodies were taken to “a site that is extremely hard to get to” in Baja California state.
The well, near where their truck and tent were found, also contained a fourth body that had been there much longer, she added.
Australian Prime Minister Anthony Albanese said on Tuesday he had requested an opportunity to speak to Mrs Robinson and her husband Martin.
“This is a terrible tragedy and my heart goes out to them,” Mr Albanese said.