Prime Minister John Key has been appalled by recent cases of animal cruelty, his office says, and the Government will consider backing a members' bill seeking stronger penalties.
National MP Simon Bridges' bill would lift the maximum jail term for cruelty offences from three years to five years.
A spokesperson for Mr Key says Mr Bridges' bill may be considered as early as Tuesday's caucus meeting.
Last Tuesday, 33 dogs were killed near Wellsford, north of Auckland, in what has been described as a frenzied shooting.
A day earlier, a man admitted in the Gisborne District Court to throwing five kittens to his pitbull terrier to kill.