The US will resettle only a few hundred refugees from Nauru, and only families, under the deal arranged with the Australian government, Sky News has reported.

The US and Australian governments earlier this month announced an unspecified number of refugees on Nauru or Manus Island would be resettled in the US, with the assistance of the UNHCR. There were reports about 1,600 refugees would be involved.

There have been consistent questions about how many would be accepted and whether the deal would even go ahead under an administration led by Donald Trump, who campaigned on a ban on Muslim immigration. Senior Republicans have also criticised the deal.

However on Tuesday Sky News, citing US government sources, said the US would take just 300 to 400 people, and only those in family groups.

According to the report, officers from the US Department of Homeland Security would arrive on Nauru this weekend to begin their own processing of applicants, and it was not expected to be finished until well after President-elect Trump is inaugurated in January.

If only families are accepted then none of the detainees on Papua New Guinea’s Manus Island – all single men – will be eligible, and the Australian and PNG governments remain at an impasse about how to close the detention centre.

Australia’s immigration minister, Peter Dutton, dismissed the report and said the US had put a number to the Australian government but detailing any specifics could be used as “propaganda” by people smugglers.

“If you put yourself in a position where new arrivals are filling the vacancies, that is a nightmare scenario,” he told Sky News. “The reports about the 300 number are completely false.”

Sky News reporter Laura Jayes and cameraman Josh Brown spent three-and-a-half days on the island last week, becoming just the third Australian news outlet to do so since the Nauruan government clamped down on media visits.

Jayes said after the broadcast Sky News applied for the visa through normal channels, without assistance from the Australian government. She said the $8,000 visa fee was waived.

David Adeang, the Nauruan justice minister and acting prime minister, told Sky negative and “skewed” reporting by some Australian media outlets affected Nauruans and that was why the government had stopped media visits.

He said to counter the effect the Nauruan government “selectively” brought in other Australian media organisations “to provide a balanced report”.

According to Jayes’ report, there have been mixed reactions to the US deal among refugees, including widespread scepticism and fears among some Muslim men about going to “Trump’s America”.

When asked about those fears, Dutton responded: “Well, stay on Nauru for 20 years, that’s your option.”

Jayes reported Nauruan authorities were preparing for any increase in tensions or acts of protest and self harm as news of the US decision progressed. She reported claims that advocates had warned refugees not to sign the deal.

Hassan Sowaid, a senior engagement officer with Border Force, said they had also heard the reports, but more than 900 expressions of interest had been registered so far, from the 1,150 people on the island.

“This is a deal, it’s a one-off arrangement. If you don’t accept the US as an outcome then frankly you are not genuine about your case going forward,” said Dutton.

“If you have family in Australia we will help repatriate those people to be with you in the United States or a third country we enter into an arrangement with, but you are not coming to our country to settle.”

Jayes visited the accommodation centres as well as schools, hospitals, and other facilities, finding the tents to be hot, cramped and mouldy, and community housing to be basic but better than most Nauruan homes because it was comparatively newer. She interviewed asylum seekers, refugees, staff, service providers, Nauruan locals and authorities, and Australian officials.

One man, Adnan, alleged he was given paperwork for his family to accompany his wife to Australia for her medical treatment, but was told the next day she had already been sent on an emergency flight.

His 13-year-old son is depressed, on anti-depressants, and does not leave his bed except to go the the bathroom, Sky reported. His 20-month old daughter was born in detention. If his wife does not return to Nauru the family cannot apply for US resettlement.

Sky also reported a case currently being investigated by police of a 30-year-old male refugee who allegedly raped a Nauruan girl, under the age of 16.

Jayes also put to Nauruan police frequent claims that they were unable or unwilling to adequately investigate incidents of assault, abuse or theft against refugees and asylum seekers.

There have been a number of cases on Nauru involving people who say police have not adequately investigated or prosecuted such crimes, including the parents of a six-year-old who was allegedly sexually assaulted by another refugee.

In what appears to be the first case relating to alleged abuse of an asylum seeker that has made it to Nauru’s courts, police charged a man with the indecent assault of a six-year-old asylum seeker last month.

Deputy police commission Kalinda Blake said most accusations were fabrications, and that Nauruan police “tend to investigate right up until the end, and then the complainants themselves come and say they … don’t wish to go ahead, they don’t wish to give us their statement”.

“Without their statement we cannot go ahead.”