Prime Minister John Key has called for the talkback host Michael Laws to apologise to the Governor-General.
During his RadioLive talkback show last Monday, Mr Laws said Anand Satyanand was "a large, fat man", and that "that seemed slightly incongruous on an Indian".
The Governor-General, who has Fiji-Indian heritage, was also the target of comments earlier that day by Paul Henry, who implied on TVNZ's Breakfast programme that he was not a real New Zealander.
Mr Key was quick to respond on Sunday to news of Michael Laws' comments.
He said the comments were totally inappropriate and there has to be respect and dignity shown to the Governor-General and he's disappointed that Michael Laws has failed to do that.
Mr Key said there was no place for personal attacks and constitutionally it's extremely difficult for the Governor-General to defend himself.
He said he believes Michael Laws is out of line and should offer an apology to the Governor-General.