Parliament is sitting under extended hours to complete a number of Treaty of Waitangi settlements.
The settlements include apologies from the Crown for historic events in which there was loss of life, imprisonment without trial, summary execution of prisoners and confiscation of land.
The four bills being debated on Thursday cover settlements for Rongowhakaata, Ngai Tamanuhiri, Ngati Makino and descendents of the Maraeroa A and B Blocks.
Maori Party co-leader Tariana Turia told Parliament the history of the Maraeroa blocks is one of grave injustice and dispossesion.
Financial redress for the iwi claims range from $11 million to $22 million.
The bills are expected to pass with near unanimous support.
Treaty Negotiations Minister Chris Finlayson says the Crown recognises that what happened to Maori in the 19th century was not good.
He says the apologies included in the settlements are not made lightly.