However in a press conference this afternoon, Mr Key told media they were "doing well".
He denied singling out the New Zealand Herald and the Sunday Star Times for criticism.
"We've got a lot of policies we're implementing. There'll always be critical appraisal of that. It comes with the territory. Doesn't bother me."
Mr Key said he expected media to become more hostile if he won a third term in Government.
"History shows you it's even more aggressive."
On Newstalk ZB this morning, Mr Key accused the New Zealand Herald of adopting a tabloid format to bolster sales.
"They have decided they need to stop their circulation from falling, or at least try and maybe go up - so they have a new editor, and the editor has turned the front page of the paper into a pretty sensational sort of front page and that's a deliberate strategy to get more sales at the dairy.''
Mr Key said the front page was "always one story, fairly sensational, and then the rest of the paper is a bit more traditional Herald, still a bit aggressive.
"They have brought David Fisher over from the Herald on Sunday, he's an investigative journalist, so called, Shayne Currie is now the editor and not Tim Murphy, and so they've got a completely different approach and they are doing that to stop the decline in sales."
Mr Key blamed increased criticism of his Government on media becoming antagonistic in their second term.
"That's just what happens, the pressure comes on Governments more because the media become more antagonistic, it just is what it is.
"I don't mean that as a complaint, I'm not moaning about it, it's just a statement of fact."
Herald editor-in-chief Tim Murphy, via Twitter, dismissed Mr Key's comments as "a 2nd term thing''.
Mr Murphy recalled that former Prime Minister Helen Clark accused the Herald of a "tabloid beat-up over, of all things, the $11b leaky buildings scandal. Plus ca change ...''
"Lange called us a #%^& tabloid in celebrated msg to editor's landline in '89. Bolger, Clark also dark. A 2nd term thing."
And he added: "Next up, PMs start talking about themselves in 3rd person. Always happens.''
Mr Key appeared on talkback host Leighton Smith's show after cancelling his weekly interview with TV3's Firstline this morning, without giving a reason, according to host Rachel Smalley on Twitter.
During his appearance on Smith's show, Mr Key also commented on the controversy over Kim Dotcom's donations to John Banks' Auckland mayoralty campaign fund, claiming Mr Dotcom was speaking out because he was angry with Mr Banks.
"He's angry with John Banks because we didn't approve the purchase of his property. I have never met the guy,'' said Key.
And he reiterated his support for Mr Banks.
"I don't need to know all the ins and outs and I don't because all I need is a clear assurance he hasn't broken the law.
"The Local Electoral Act, which is the act that governed taking of donations for the mayoral campaign is a very liberal and loose act.''
He also commented on the proposed SkyCity convention centre.
"When I came in as the incoming Minister of Tourism in 2008 they said to me 'build more infrastructure', if you want to take lumps out of tourism, the peaks and troughs, build a convention centre and other infrastructure.''
Mr Key says of the five deals received through an expression of interest, four asked the Government to pay for the entire construction.
"SkyCity said 'here's a deal where we get more pokie machines and other minor changes to our license in return for no cash injection'.''
According to the Prime Minister, reaction before the election was positive - including from Labour.
"Now they're trying to change the argument and say 'it's about problem gambling'.''
He said he believed people would gamble on the internet if there were no pokie machines.
Mr Key defended criticism of his party's tax cuts and said New Zealand had made strides to close the gap between rich and poor, with an 11 per cent increase in after-tax wages since National was elected.
