Mr Morgan said it was an opportunity for the tribe to talk to the government, to address the unresolved interests of Waikato Tainui and the Kingitanga into Tamaki.
It was hoped the claim would be resolved by this time next year.
A spokeswoman for Mr Finlayson said the Crown recognised Waikato-Tainui was one of several groups with historical Treaty of Waitangi claims in the Auckland region.
"The minister would welcome a robust mandate strategy for Waikato-Tainui as a preliminary step towards commencing negotiations of Waikato-Tainui's remaining claims," she said.
"The Crown has not yet recognised any entity as having the mandate to negotiate a settlement of the remaining claims of Waikato-Tainui."
Treaty expert Professor Paul Moon of AUT University said it was a huge claim that could lead to a stoush.
He said there was a risk that a great deal of division could emerge between claimants - Ngaphui, Ngati Whatua and now Tainui - as they would be scrambling over who was entitled to what in Auckland.
Prime Minister John Key was among those gathered at Turanagwaewae Marae to hear King Tuheitia's speech.
Commenting on the speech, Mr Morgan said it was important for the king to be out and about amongst his people.
He said the king has struggled with his health and it lifted the hearts and minds of his people to see him among them, listening and then finally taking the pulpit.