"That totally goes against the fundamental principle that has been bought into by 99 per cent of the New Zealand population," he said.
"Yes, we have to address these historical issues. We want settlements that are just and are durable and are full and are final."
Finlayson, who is also the Attorney General, said the Government recognised in settlement a very strong personal connection that people have with various rivers.
"Our Whanganui River settlement is a ground-breaking piece of legislation.
"But there is a great step from saying people have an interest, an historical, a cultural interest in water to saying they potentially own it. That is where, in principle, I could never go."
Using the Waikato River as an example, he asked: "Is it the proposition that Tuwharetoa own from [Lake Taupo] down to beyond Huka Falls and then Te Arawa owns the water thereafter and then Ngati Raukawa and then you get further down the river and it's Waikato Tainui? Of its very nature, you can't own water."
New Labour leader Jacinda Ardern released the party's water policy last week, which included the statement "everyone owns our water".
She and environment spokesman David Parker outlined plans for the Government to charge water bottlers and others with heavy water consumption, at rates to be determined in a water summit after the election.
The royalties would be distributed to regional councils to fund improving the quality of rivers and streams, after some of the royalties had been paid to Maoridom to meet treaty settlements, Parker said.
"A share of this annual royalty would go to Maoridom. The majority would go to the regional council."
Parker, also a former Attorney General, said last night that whether you said no one owned the water or everyone owns water, "it is a blind alley which does not take you very far". Either way, those with water consents had an interest in water as did Maori, and Maori interests could be broken into two parts: the quality of the water and their claimed interest in the value of the water.
He said Maori had an unresolved Treaty of Waitangi interest in water.
Some management issues had been resolved but no Government had settled Maori rights in the value of water.
He did not have a fixed view as to whether the water issue should be addressed by iwi, or in a pan-tribal settlement similar to the fisheries settlement in the 1990s.
"If you wanted to do it in an iwi by iwi level, it is actually reasonably easy to do because all of the water takes are metered these days and so you just have to establish the rohe [area] and work out what the royalty is that is coming from that area. Nonetheless, you might want to do it on a more holistic basis."
King Tuheitia has said that Maori own the water but Parker said Labour did not agree with that.
"Everyone owns the water but some people have interests in water that others don't."
Parker said water was a taonga which was guaranteed to Maori under the Treaty of Waitangi.
"They had uninterrupted possession of all of their waterways and therefore they could use them including for value."
Maori had argued - with the agreement of the Waitangi Tribunal - that that includes an interest in the value that can be made from water.
"This is nothing to be scared of. We have worked these issues through before."
The chairman of the New Zealand Maori Council, Sir Edward Taihakurei Durie, said if legislation was put through to give effect to Labour policy, it need not open up existing treaty settlements.
"It is not a free lunch for Maori, but something that would give employment to our young people.
"We are pretty much in line with what the Labour Party is saying except we would apply it to all commercial users."
Domestic users should not pay.
