"The application is currently being assessed against the RCHF criteria along with other applications for the contestable fund," Mr Butts said.
"Announcements on funding decisions through the RCHF will be made later this year."
Earlier, Nicola Williams, chairwoman of the Trust, said a combination of donations, pledges and bequests in the final month raised more than $5 million, taking total private funding to just over $10 million.
Ms Williams said getting the application into the ministry's June funding round has been pivotal to the project.
"Other funding proposals and applications are dependent on getting the Government funding. If we had to wait until the next funding round we would have missed deadline dates for at least two major applications that are in the pipeline," she said.
Ms Williams said if the funding application is approved the trust was confident of raising a further $9 million by the end of the year to complete the project fundraising.
Developed design drawings by Warren and Mahoney Architects have been prepared and unencumbered resource consents granted. If everything goes to plan construction is due to begin in 2017, enabling the historic gallery to be reopened in time for its 100th centenary celebrations in 2019.
The proposed redevelopment includes earthquake strengthening and restoration of the gallery and development of a new purpose-built wing for exhibitions and education, as well as storage for the extensive art collection.