Mr Tu'i'onetoa was elected prime minister last week to replace Mr Pohiva, who died last month in Auckland.
He achieved this by crossing the floor and taking several members of the PTOA Party with him to form a new party with the nobles.
But local media have reported the remnants of Mr Pohiva's party as saying this was a betrayal of the late prime minister by Mr Tu'i'onetoa and his colleagues.
The new prime minister said this is wrong.
"The good governance and those good principles nobody should claim that as their own, no matter whether you are in the so-called PTOA Party or the People's Party, but if you stick to that principle that is the legacy. Nobody should claim that as their own," he said.