The US offered to resettle Australia’s refugees from Nauru and Manus Island on the understanding that in exchange Australia would “do more” to help other refugees, the US architect of the deal has said.

Anne Richard, the former US assistant secretary of state for population, refugees and migration, told Guardian Australia the US was motivated to take part because of conditions on Nauru and Papua New Guinea’s Manus Island, where refugees who had tried to reach Australia by boat were detained.

“The impetus behind the US-Australia deal on our side was to get the people who were refugees off those islands, because my understanding was that conditions were bad,” Richard said.

A group of refugees held by Australia on Nauru leave for resettlement in the US. Photograph: Refugee Action Coalition

“I’ve never been to either place but I’ve heard a lot of stories – and I’m hoping to meet with people who are resettled in the US from there – but everything I’ve read suggests the conditions are quite bad and, over the long term, unhealthy.”

The Obama administration agreed to take up to 1,200 refugees from Australia’s two offshore detention centres, and it was expected Australia would resettle some refugees – reportedly between 20 and 50 – from Central America, who were mostly fleeing gang violence.

Richard, who was in her role from 2012 to 2017, said the deal was struck with the expectation Australia would also make a greater effort to assist refugees from outside its region. Other details of the deal, signed in September 2016 and announced two months later, remain classified.

Richard said there was no agreement it would be a “one for one swap”, despite much speculation in the press.

“It was not written down in a way that lends itself to mathematical formula,” she said. “It was an expression between two close allies that Australia would make every effort to do more, to take refugees fleeing the triangle of Central America, to take refugees from outside areas it didn’t usually take refugees from, to take more from Africa, for example, where there are large numbers of refugees in the population.

“It was understood that there would be an effort but there were no deadlines.”

A group of Cuban refugees resettled in Australia in 2017 were not part of this deal but were part of an agreement from several administrations ago.

Where Canada continues to be very generous, the US and Australia have very mixed records. Anne Richard

In the two years since it was signed, fewer than 500 people from Manus and Nauru are believed to have been accepted for resettlement in the US.

Asked if she had expected the deal to progress so slowly, Richard said more refugees would have been coming in sooner if Hillary Clinton had won the 2016 presidential election. But she said it was positive that Donald Trump upheld the arrangement, despite describing it as a “dumb deal”.

“I’m very happy the deal is being honoured and that people are coming,” she said.

Many refugees have been refused by US authorities, and some have not applied for reasons including having family in Australia, or fear of living as a Muslim in the US. Advocates have speculated that Trump’s travel ban on nationals of some countries is behind the very small number of Iranians among accepted refugees, and the lack of any other nationals from other listed countries.

The state department has told Guardian Australia the travel ban does not apply to its refugee programs but said there were increased security screenings for refugees in response to another of Trump’s executive orders.

“I’m very opposed to the travel ban, to the thinking or lack of thinking [involved],” Richard said. “I’ve joined with other national security veterans … to offer court briefs explaining that it didn’t make sense.

The US president, Donald Trump, discusses the refugee deal with Australia with the former prime minister Malcolm Turnbull. Photograph: Pete Marovich/EPA

“You’re really supposed to analyse the individual’s case and not treat entire groups of people as somehow too dangerous to bring to the US. There is no connection between people who have carried out terrorist attacks in the US and the groups that are discriminated against by the travel ban and advanced vetting.”

Richard, who will be in Australia next week to deliver the keynote address to the Kaldor Centre conference, was highly critical of the current US government’s approach towards its humanitarian responsibilities.

“For me, the important thing is they have changed … how we identify ourselves. Who we are has somehow been jettisoned.”

The US has wound down the number of refugees being accepted. In the last year of Obama’s presidency the US accepted 84,994, and had proposed taking 110,000 the following year.

Under Trump it dropped to 53,716 in the first financial year, and while he was then criticised for cutting the official ceiling to 30,000, Richard said the US did not even reach it, taking only 22,491.

In 2016-17 Australia took the largest number of refugees since the start of its humanitarian program – 24,162, which included a special intake of Syrian and Iraqi refugees.

However, it has maintained its hardline against anyone who seeks asylum by boat – deploying a three-pronged military strategy including joint pre-departure operations with foreign authorities, using customs vessels to turn boats around at sea and detaining asylum seekers on Manus and Nauru.

“What I was familiar with [when in office] was that the UNHRC really counted on the US, Australia and Canada as the leaders in resettling refugees, we were kind of the good guys,” Richard said.

“When I met Australian counterpart overseas, and same with the Canadians, our talking points generally aligned in the things we were trying to accomplish. I think that’s changed. Where Canada continues to be very generous, the US and Australia have very mixed records.”