Mr Key was asked to withdraw his comments, but only after the urging of Green Party co-leader Russel Norman.
Mr Mallard told reporters afterwards that Mr Carter had begun his tenure well in February, but had become increasingly biased.
He urged Mr Carter to meet with previous Speakers such as Lockwood Smith to educate himself on how to control the House.
Leader of the House Gerry Brownlee said Speakers were traditionally more lenient on the Prime Minister and the Leader of the Opposition.
He said the ejections were warranted: "All Speakers have to stamp their authority on the House at some point."
He said Mr Carter was doing a "very good" job and Mr Mallard's arguments were "political posturing" because he had wanted the Speaker role himself.
Last week, Dr Norman wrote an open letter to the Speaker warning that question time would become increasingly chaotic if ministers were not made to answer direct questions.
LIVE STREAM FROM PARLIAMENT:
can't see the video? please click here