Prime Minister Malcolm Turnbull has launched a stinging attack on Kevin Rudd, accusing the former PM of verballing him and plotting in advance to leak private correspondence to the media.

Mr Turnbull denied he supported Mr Rudd's tilt to lead the United Nations during a key December meeting, but refused to be drawn on Mr Rudd's central claim that he had previously expressed his support for the bid.

Asked specifically about that claim on Monday afternoon, Mr Turnbull equivocated.

"I'm not going to be getting into this debating Mr Rudd ... he and I have had discussions that have touched on this over a long period of time," he told ABC radio.