Labor has hardened its position against draft migration laws out of concern of a diplomatic clash with New Zealand, while picking two other fights with the Morrison government after claims it was "capitulating" on policy.

Labor is demanding the government modify a new character test it wants to insert into the Migration Act to allow the deportation of convicted criminals even when they have lived in Australia for decades.

New Zealand PM Jacinda Ardern has publicly warned of the "corrosive" impact of tensions with Australia over its migration laws. Credit:AP

Opposition home affairs spokeswoman Kristina Keneally is seeking three changes to the government bill, including concessions to address warnings from New Zealand Prime Minister Jacinda Ardern about the "corrosive" rules.

The dispute appears likely to put the migration bill in limbo in the Senate with Labor holding out against the changes while the government struggles to secure crossbench support in the months ahead.