More than 1000 people arrived yesterday for the hui, including many of the grassroots providers of the kohanga reo as well as the full board.
Trust board members will almost certainly lose the right to be appointed for life in the proposed changes.
The board is also expected to promote a more accountable structure rather than be seen to have one foisted on it by the Government.
The board says it has been working on models for change for four years.
But Ms Parata and Maori Affairs Minister Pita Sharples have set the April 30 deadline to hear back from the trust on its planned changes.
In a letter to the trust, they say it has lost the confidence of the Government and the public.
The ministers say they will assure kohanga reo that they will continue to receive their operational funding but threaten to curtail the trust's current role, which is set out in a contract due to expire on June 30.
They tell the trust in the letter that Secretary of Education Peter Hughes will be initiating discussions "on whether a new contract proceeds and what form may be agreed".
The ministers say they would be willing to discuss a short-term extension of the contract to October 30 while discussions were under way.
"A resolution that reflects 21st century governance, including representation, transparency and accountability, is necessary to restore public, whanau and government confidence," the letter says.
The Government has already suspended negotiations with the trust until it modernises its structures, and the letter sets out the conditions for talks to start, including democratic representation of kohanga reo and elimination of board appointments for life.
The media have been banned from the hui. Mr Morgan could not be reached last night.