Mr Joyce and Mr Dunne are the first ministers to speak on the issued after police minister Michael Woodhouse labelled it an "operational" issue and refused to comment. Justice minister Amy Adams, who formulates policy based on crime data research, also would not comment.
Mr Joyce, who is also innovation minister, endorsed the role of academics, saying their legal responsibility role in the Education Act as "critic and conscience of society" would be unchanged in the current and future reviews of the legislation.
He also took Opposition politicians to task as being "mischievous and incorrect" over claims access had become restricted under a National government.
"There has also been no change in Government policy in regards to Government agencies supplying information to academics for research purposes. The same policies that apply now applied under previous Governments."
Mr Joyce said each agency would have a policy around access to sensitive information "but as Science and Innovation Minister and Tertiary Education Minister I'd encourage them to be as open with their data as is reasonably possible".
Mr Dunne, who is United Future leader, said he had written to Mr Woodhouse, asking that Police Commissioner Mike Bush be instructed to have the decision banning Dr Gilbert reviewed. Police have since confirmed it is currently under review, with Dr Gilbert being told next week whether the ban would be lifted.
He said the general constraint of researchers was "unacceptable". "The whole thing is absurd. I think the police need to review it."
Dr Gilbert said it was "nice" to hear ministers speak on the issue but he hoped Mr Woodhouse or Ms Adams would also express a view. "It's got huge policy implications and that should be addressed at a political level."
Police have stood by the contract, although said it is subject to "ongoing review".