Details of the conversation emerged on Friday when The Washington Post published the full transcript of the call, which included a heated discussion over the refugee swap deal brokered between Turnbull and the Obama administration.
Imran Mohammad told the Human Rights Law Centre he broke down in tears when he read the transcript.
"Their words made me feel like I am just a product to them and I can be traded for anything," he said.
"I am just a human being and there is no need to play with my life."
The U.S. agreed to take up to 1,250 refugees from the Australian processing centres on Manus Island and Nauru in exchange for refugees from Central America. However, Friday's leaked transcripts revealed that Turnbull assured Trump the U.S. could honour the deal without taking any refugees from Manus or Nauru.
"It [the deal] does not require you to take any," Turnbull said. "The obligation is for the United States to look and examine and take up to and only if they so choose."
"You can decide to take them or to not take them after vetting. You can decide to take 1,000 or 100. It is entirely up to you. The obligation is to only go through the process."
The transcript also revealed Trump doubts those held on Manus and Nauru are genuine refugees.
"I guarantee you they are bad. That is why they are in prison right now. They are not going to be wonderful people who go on to work for the local milk people," he said.
Turnbull also referred to the people held on Manus and Nauru as "economic refugees" during the phone call, despite the Department of Immigration and Border Protection confirming in their June update that an overwhelming majority were found to be legitimate refugees.
The Australian government recently cut water and electricity to the major compounds on Manus Island as it begins to close the facility, after the PNG Supreme Court ruled it illegal.
Some refugees are refusing to leave the Manus detention centre, saying they are scared for their well-being.
Two men, who had been relocated from the Manus detention centre to East Lornegau, were attacked with machetes and seriously injured last week.
Over 2,000 people remain housed in the Manus and Nauru processing centres.Suggest a correction