The federal government has spent an additional $22m in supporting the US deal to resettle a number of refugees currently held in Manus Island and Nauru regional processing centres, published documents have revealed.

The documents also reveal the secretary of the Department of Immigration and Border Protection flew to the US at a cost of more than $32,000 to discuss the deal with US officials.

Responses from the department to questions on notice from February’s Senate estimates hearings were received last week and published online without announcement on Tuesday.

Among dozens of requests, the Labor senator Kim Carr had asked for the cost of “any extra funding that was allocated to border enforcement or operation sovereign borders following the signing of the US refugee agreement”.

The department’s response included an extra $7m for maritime and aerial surveillance as well as $15m for “on-water assessments, air transfers, regional command travel costs and strategic communications offshore”.

The US deal was struck between the Australian federal government and the previous US administration under Barack Obama. The current US president, Donald Trump, publicly rubbished the “dumb deal” in February and, last month, his vice-president, Mike Pence, told Australian media his government didn’t “admire” it but would honour it.

The immigration minister, Peter Dutton, had not spoken directly with any officials from the Trump administration after the president’s public comments and there had been no attempt by Trump or Dutton to alter the arrangement, the department said.

Before Trump’s inauguration, the secretary of the department travelled to the US in December to discuss the deal with US officials. According to answers released this week, the cost of the five-day December trip totalled $32,316, including more than $26,000 on airfares.

The department said the discussions were “part of a broader program aimed at enhancing Australia–US cooperation”.

The cost of a second visit in January, which was “part of a broader multi-national visit”, was not disclosed.

Details about the US refugee deal, including the date it was signed and by whom, were refused to Senate estimates, citing confidentiality provisions between the two governments.

Similarly the department refused to provide details about Australia’s agreement to take refugees from Costa Rica but denied it was a “people swap”.

However, it did disclose there were no financial elements to the US deal and that Australia was not asked to provide any settlement service support to people who were accepted by the US.

The department and Dutton have repeatedly declined to provide details about the deal and how it will operate, beyond confirming an “indicative planning number” of up to 1,250 people. There are no guarantees the US will take anyone.

US officials have visited both Nauru and Manus Island and, according to the Australian department, by 22 March this year 1,626 people had expressed an interest in US resettlement.

This comprised 228 women, 1,253 men and 145 minors, including 24 people who were currently in Australia.

The department said the most vulnerable refugees – with an “initial focus” on women, children, and families – were the priority and the US was applying “rigorous assessment and vetting processes”.

The federal government has not said what it will do if the US does not take all refugees from Manus Island and Nauru. It has repeatedly claimed to be in discussions with third-party countries but no arrangement has eventuated.

The department repeatedly relied on a public interest immunity claim to not provide information, including which countries it had spoke to, and asked why it had not accepted a longstanding New Zealand offer to take 150 people a year. The department said the government “will not undertake activities that could be used by people smugglers as marketing opportunities”.

The department also continued to point to PNG’s offer of resettlement and Nauru’s 20-year temporary refugee visas as a contingency measure.

It was also disclosed that in 2016 the immigration department spent almost $43m on external legal services, $313,738 on social media, more than $1.06m on web design and almost $81,000 on “acting or public speaking training”.

The department of immigration and Dutton’s office have been contacted for comment.