The last four children living in Australian government-run offshore processing on Nauru have now left the island, amid a group of 19 people flown to the US for resettlement.

The group includes a number of Iranians, according to refugee advocates, contradicting persistent suspicions that Donald Trump’s travel ban on six nationalities was blocking refugees from the resettlement scheme.

Another 22 men from Manus Island were also transferred to the US.

Estimates suggest the US has now resettled about 500 of Australia’s refugees since the deal between the two countries was signed in late 2016. The US has said it would take up to 1,200, but advocates and refugees have become distressed at the pace, as well as frequent rejections.

“The US deal is glacially slow,” said Ian Rintoul of the Refugee Action Coalition.

“At the present rate of resettlement, it will be another four years before the remaining refugees would be resettled in the US.”

According to the Australian-run refugee support group Ads-Up (Aussie Diaspora Steps Up), one of the Nauru families has flown to Colorado and another to Texas. All are expected to repay the cost of their transfer to the US within four years.

“It’s really hard on families. There’s one family … their debt is US$12,000,” said Fleur Wood, the cofounder of Ads-Up, which connects Australians living in the US with recently resettled refugees from Manus Island and Nauru, providing support and friendship.

“A debt like that is overwhelming for refugees. They have four years to pay it off but when you’re earning $7 an hour … a debt like that is really crippling. It stops them being able to do things to get ahead in life.”

The US state department has been contacted for comment.

Australia’s immigration minister, David Coleman, said the transfer illustrated a successful approach to border policy.

“This is something the government has been working on for some time, quietly and in a way that would not impact our border protection policies,” Coleman said.

“Our track record on this issue is clear and it is a massive contrast with what was seen under the previous Labor government.”

“By weakening our borders, Labor put more than 8,000 children in overcrowded onshore detention centres and in regional processing countries.”

The Australian government has repeatedly claimed it had removed all children from detention. Children on Nauru were no longer technically living in detention, as families had moved to community accomodation near the centre.

Widespread cases of mental and physical illness continued among the population of refugees and asylum seekers, and late last year an intense campaign by charities, businesses and NGOs called for all children and their families to be taken off the island.

One of the architects of the US deal, then US assistant secretary of state for population, refugees and migration, Anne Richard, has previously told Guardian Australia the US was motivated to get people off Manus Island and Nauru because of the widely reported conditions which were “quite bad, and over the long term, unhealthy”.

The US made its offer on the understanding that in exchange Australia would “do more” to help other refugees.

In August, when Scott Morrison became prime minister, there were 109 children still on Nauru.

Around 970 people remain across the two islands, including 154 who have not been found to be refugees. Senate estimates earlier this month revealed more than 1,240 people have been transferred to Australia for medical treatment since 2014, and only 282 have returned.

In many cases people were brought to Australia for urgent treatment only after legal intervention – with the department transferring them either on agreement before it reached court or under court orders after having argued against the transfer request.

This financial year the department has spent $1.373m responding to the legal interventions. In the previous financial year the department spent $275,000.

Labor’s immigration spokesman, Shayne Neumann, said the resettlement of the last refugee children from Nauru was “good and overdue news” but he criticised a lack of any “long-term plan” for the hundreds now in Australia.

“Scott Morrison and Peter Dutton have absolutely failed to secure viable third-country resettlement for people on Nauru and in PNG for close to six years, leaving them to languish in indefinite detention because of these failures,” he said.

“Australians understand our nation can be strong on borders and still treat people humanely.

Morrison should start by immediately accepting New Zealand’s offer to resettle refugees and negotiate appropriate conditions similar to those under the US arrangements, he said.

In a bilateral meeting with the New Zealand prime minister, Jacinda Ardern, last week, Morrison said his government had no intention of accepting the country’s offer.