The Obama administration urged Australia to change its policy of offshore detention of refugees while agreeing to accept up to 1,200 people to relieve their suffering, a former senior US official has said.

The former US deputy secretary of state Heather Higginbottom, who negotiated the deal designed to take refugees from offshore detention on Manus Island and Nauru, makes the revelation in a Time magazine article.

Higginbottom penned the article to address the leak of the full transcript of the phone conversation between US president, Donald Trump, and the Australian prime minister, Malcolm Turnbull, about the deal.

In the January phone call Turnbull persuaded Trump to honour the Obama-era agreement, despite protestations from the president it was a “stupid” deal that would “kill” him politically. Turnbull also falsely claimed that people held in Australia’s offshore detention centres were “economic refugees”.

Higginbottom said the refugees were “people who risked their lives on makeshift boats to flee conflict and the lack of access to basic means of survival but were turned back by an Australian government that refuses asylum seekers who arrive by sea”.

“While the last administration strongly pressed the Australian government to change its policy toward asylum seekers, we also sought to immediately relieve the suffering of these refugees and agreed to resettle up to 1,200 after they went through the US government’s rigorous refugee screening processes,” she said.

Higginbottom, who is now the chief operating officer of the aid organisation Care, singled out the “policy of detention” as the aspect of Australia’s policy rejected by the Obama administration.

Higginbottom lamented that coverage of the Turnbull-Trump phone call had focused on personalities and not that “the wellbeing of 2,000 actual human beings hangs in the balance”.

The United Nations has called Australia’s policy of offshore detention of asylum seekers unjustifiably punitive and unlawful, “cruel, inhuman and degrading treatment”.

In the leaked phone call, Turnbull told Trump that Australia had “taken a very strong line on national security and border protection” and said that he, Jared Kushner and a White House immigration adviser had “reflected on how our policies have helped to inform your approach ... We are very much of the same mind.”

Turnbull noted that Trump, who has attempted to ban immigration from certain Muslim-majority countries, prioritised “minorities” in his executive order and linked it to the fact 90% of the 12,000 refugees Australia had accepted from Syria were Christians.

Turnbull explained that Australia turned back boats at sea and sent asylum seekers to offshore detention “not because they are bad people” but rather to prevent people-smugglers of a “product”.

He said people who came by boat would not be let in even if they were a Nobel prize-winning genius, which prompted Trump to say “that is a good idea”.

“We should do that too,” he said. “You are worse than I am.”

Turnbull referred to a speech he gave to the UN in September claiming that Australia’s harsh treatment of refugees was necessary to control its borders and maintain support for its regular migration intake.