Mr Key yesterday said he had ordered a "government inquiry" - but only into the former Justice Minister's relationship with former Serious Fraud Office boss Adam Feeley.
The suggestion by Whale Oil blogger Cameron Slater in a leaked 2011 email that she was "gunning" for Mr Feeley prompted her resignation on Saturday.
Mr Key said Mr Peters had "lots of bottom lines ... This is just another one".
But he would not rule out widening the inquiry after the election.
Asked whether he would rather go into opposition than set up a broader inquiry, he said: "You need to ask me all of those questions after the election."
Mr Key maintains a broader inquiry into the Dirty Politics allegations isn't warranted and the Opposition push for one is politically motivated.
He said the terms of reference for his government inquiry would be made public within the next few days.
But Labour yesterday set out the terms of reference it wants for the inquiry.
They include central allegations made in Hager's book, such as the 2011 release of SIS documents to Slater to embarrass then-Labour leader Phil Goff, the alleged unauthorised access of Labour's online membership database by Mr Key's former senior adviser Jason Ede, and Ms Collins passing information about senior public servant Simon Pleasants to Slater.
Labour says the inquiry should also examine Ms Collins' conduct in relation to Oravida, the export company her husband works for which was at the centre of conflict-of-interest claims against her this year.
Labour's deputy leader, David Parker, told reporters yesterday afternoon that he believed the Oravida issue had been included because "it's part of a pattern, isn't it?"
"I think there's plenty of unanswered questions there."
Labour has also filed a complaint with the police over allegations of a conspiracy to defeat the course of justice in undermining government departments, inappropriate use of information on Mr Pleasants, and Mr Ede's accessing of its database.