The Maori Party is yet to decide which option it prefers as a replacement for the Foreshore and Seabed Act.
The National Government on Wednesday outlined four possibilities, clearly stating its preference that no one would own the land, and iwi would regain the right to go to court to establish customary title.
Its preferred option would also mean customary title would be defined by law, any such land could not be sold and public access would still be guaranteed.
The Maori Party is being coy about its preferences, saying the public domain proposal is just one option.
Party's co-leader Tariana Turia says its main concern is about repealing the current law and access to justice and it is now up to the people to have their say on the proposals.
"Our main concern is around repeal, about access to justice and about our people's ability to take it to court."
Other options include keeping ownership with the Crown, or giving Maori absolute title. The public has until the end of April to make submissions on the discussion document.
The Green Party says the Government's foreshore and seabed proposal is not a victory for Maori. Co-leader Metiria Turei believes the timing of the consultation period is unfair.
Govt proposal not yet acceptable - iwi
Iwi leaders say the Government's proposal that no one should own the foreshore and seabed is a significant advance, but not yet acceptable.
Mark Solomon of Ngai Tahu, who chairs the influential Iwi Leadership Group, says the Government's proposal to repeal the 2004 Act, give up Crown ownership and allow Maori to go to court establish customary title is a great step forward.
But a commentary written by the group says putting the foreshore and seabed into public domain may not satisfy the rights, expectations and values of iwi and hapu.
It says the proposal does not explain who will get the right to develop and mine below the high-water mark.
Mr Solomon says despite its problems, the proposal contains good elements and can be seen as a useful stepping stone to a lasting solution.