Yesterday at Parliament, Mr Kenrick - facing MPs' questions about the affair - said staff already had to submit an annual declaration on conflicts of interest.
"My personal view is we should expand that to be more specific about participation in political parties."
Later, he said the broadcaster "will probably need to be more robust in terms of how we identify political allegiances, particularly within our news and current affairs areas but [also] across the business as a whole".
But the conflict of interest section of TVNZ's 2011 Journalists' Manual says party memberships must be declared if public knowledge of them is likely to affect perceptions of impartiality.
The rules also say those who, like Mr Taurima, return to work after unsuccessfully seeking public office "can nevertheless remain tainted in the minds of viewers".
Mr Kenrick was asked yesterday by National MP Chris Tremain if TVNZ was "a breeding ground for Labour Party activists".
He replied that his personal view was "we had some poor judgment by some individuals".
"To extrapolate that into a cultural issue for our entire Maori and Pacific department, let alone the organisation as a whole, is something that I don't think is founded," he said.
Meanwhile, TVNZ said news and current affairs boss John Gillespie had completed talks with staff involved in the controversy over veteran newsreader Peter Williams and Seven Sharp reporter Dean Butler making up abusive tweets for a story on cyber bullying that went to air and was "satisfied with the outcomes".
TVNZ's current guidelines on political activities
• "Someone working in news or current affairs should ask the basic question: If this fact (party membership) became public, would our viewers regard the journalist involved as truly impartial? If there is any suggestion they would not, then it must be declared."
• "Despite every effort to remain objective, journalists who return to work after being unsuccessful as political candidates can nevertheless remain tainted in the minds of viewers and therefore be judged to have lost their impartiality ... anyone with political aspirations must consider the serious risk of conflict and the need to refer upwards."