Mr Finlayson told the hui that he was not there to "pressgang anybody" into a large group cluster.
LGC is how the Treaty of Office Settlements progresses claims, by bringing claimant parties together in sizeable groups for negotiations.
Uenuku iwi chairman Aiden Gilbert said the protest was over iwi fears that land alongside the Whanganui River and its tributaries would be included in the river claim.
"We are the invisible party. We only had four days' notice of the initialling, and we are not happy with the timeframes and lack of transparency," Mr Gilbert said.
Some Uenuku members had travelled from Kaitaia, Tauranga and Hamilton to be in Wanganui yesterday.
Uenuku board member Tukaiora Connell, who travelled from Te Tai Tokerau to address the minister, said they wanted to know why Uenuku was not included in the negotiation around the deed of settlement.
Another, Rangi Bristol, said Uenuku had been alienated from their lands and their heritage.
"We own that land right beside the river," he said.
Gerrard Albert, a member of the Whanganui River Trust Board negotiating the river claim, said no land reserves that bordered the river or its tributaries were included in the deed.
The trust board negotiators would now hold hui with Whanganui iwi over the next three weeks to discuss ratification of the deed of settlement.
