The Turnbull government signed an agreement to make a $640,000 grant to Bjørn Lomborg’s Copenhagen Consensus Centre nine months after plans to establish the centre had been abandoned.

The education department may have been under no legal obligation to make the grant, documents suggest.

The funding was used to support the centre’s post-2015 UN development goals project that found limiting global temperature rises to 2C was a poor investment.

A breakdown of costs released on Thursday shows that $482,000 of the Australian funding was spent on professional fees and services including research, “outreach” and forums.

About $146,000 was spent on travel in an ambitious global project convening seminars to discuss the UN development goals in Bangladesh, Brazil, Colombia, India, Indonesia, Kenya, Mexico, Nigeria, South Africa and New York.

The project formed the basis of Lomborg’s book The Nobel Laureates’ Guide to the Smartest Targets for the World, which is not widely available in Australian shops.

Documents released under freedom of information show the department only entered a formal agreement to fund the project as late as 21 March 2016. Based on those documents and answers provided by the education department it appears the government did not have any ongoing commitment to the project when the Australian Consensus Centre was canned in June 2015.

The government’s plan to establish the Australian Consensus Centre was put into effect in an agreement with the University of Western Australia (UWA) dated 24 March 2015.

But on 26 June 2015 the government and UWA terminated the agreement by consent because the university rejected the funds after a public backlash. The agreement created an obligation for the government to pay UWA’s reasonable costs, but did not create obligations to the CCC.

An education department spokeswoman told Guardian Australia no payments were made to UWA under the agreement.

The $640,000 grant is disclosed in a log of education grants dated 2 July 2015 but the spokeswoman said it was only added after the grant agreement was signed with the CCC on 21 March 2016.

In September 2015 it was referred to in an incoming ministerial brief to Turnbull’s pick for education minister, Simon Birmingham.

“The department has negotiated a funding agreement which will provide a one-off payment to the CCC for a total of $640,000 to cover costs incurred in relation to the establishment of the Australian Consensus Centre prior to the decision to cancel this project,” it said.

When Guardian Australia asked for a copy of the “funding agreement” with the CCC referred to in the briefing, the education department provided the 21 March 2016 agreement.

An education department spokeswoman said “payments were undertaken in accordance with the government’s funding agreement with UWA and the memorandum of understanding between UWA and the CCC”.

The department did not directly respond to questions about how an agreement between the government and UWA and a the memorandum between UWA and the CCC could create legal obligations between the department and the CCC.

If there was another legal obligation to pay the CCC, such as an equitable duty, the education department did not identify it after detailed questions, nor identify its source.

Neither the education department nor Birmingham explained why a new grant agreement was struck on 21 March 2016 if all or part of the $640,000 was owed by the commonwealth for some pre-existing legal obligation.

Asked if the $640,000 was to pay for costs incurred, as described in the brief, the education department spokeswoman said: “The government’s decision to pay the grant was based on the merits of supporting further work to complete the project.

“Costs for the project had been incurred. However, under the funding agreement, the department required additional work to be undertaken.”

Labor’s innovation, industry, science and research shadow minister, Kim Carr, called on the government to provide a full explanation of the grant.

“The government must explain how and why this grant was still awarded, even after it had terminated the agreement with the university for the Australian Consensus Centre following pressure from the opposition and the research community,” Carr said.

“Malcolm Turnbull cannot hide behind a prior deal made by Tony Abbott – his government signed a fresh contract on 21 March 2016.”

“This use of taxpayers’ money to promote an anti-science conservative agenda shows that Malcolm Turnbull is still beholden to the right wing of the Liberal party.”

At Senate estimates on 20 October, Birmingham said the government had made a “special purpose” decision to allocate funding to the consensus centre, a process that was “terminated”.

“Special purpose funding was allocated prior to [Christopher] Pyne deciding to terminate the process … It was commenced under Pyne’s tenure as well,” he said.

“The decision to initiate it and also the decision to terminate it occurred prior to my appointment as minister. So you are trawling over some ancient history really.”

Asked at estimates what the “special purpose” for the grant was, Birmingham said “obviously the government honoured the contractual obligations insofar as it was obliged to” at the time the centre was cancelled.

A spokesman for Birmingham told Guardian Australia his answers to estimates were factual and not misleading but refused to explain what “contractual obligations” the commonwealth had to the CCC before striking the new agreement on 21 March 2016.

A spokesman for the CCC referred Guardian Australia to the education department. UWA refused to comment.