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Prime Minister John Key's son has been suggested again as a recipient for the worthless shares of senior National Party ministers.

Last week during question time the Prime Minister was asked about his shares in Jackson Mining, an Australian company that does not operate in New Zealand, and he answered that he had tried to sell his shares.

"I bought the shares in 2001, and the last time I looked at them, from memory, was 2007 or 2008. At the time they were trading at 3.5c, and when I offered them to my son, who was 12 at the time, even he didn't want them."

Yesterday blogsite revealed Foreign Affairs Minister Murray McCully held shares in Widespread Portfolios, a New Zealand investment company with mining interests at home and overseas.

The Government is drawing up a discussion document about the prospect of mining in parts of the conservation estate.

Yesterday Mr McCully downplayed the significance of the shares, saying he had tried to sell them and would continue trying to sell them.

"They've been in my hands since about the year 2000. I declared in them in the appropriate fashion, there are a total of 184 shares and their market value is approximately $31.63.

"I'll have to give them away. Maybe the Prime Minister's son will be interested. It's been an unmarketable parcel and I'll have to give them to somebody."

Mr McCully denied there was a conflict of interest because he had declared his shareholding in the register of pecuniary interests, and had not been present at any Cabinet discussions about mining.

Opposition leader Phil Goff said any shares in a mining company working in New Zealand represented a conflict of interest.

"Whenever there was a conflict of interest of any sort in the Cabinet I was part of, a minister was expected to remove him or herself from the room immediately and not participate in those discussions."