Federal Labor MPs have begun circulating an email critical of former prime minister Kevin Rudd, in a sign of continuing tension within the party.

The email, which was sent to Mr Rudd this morning and copied to some of his colleagues, accuses the former Labor leader of being "childish" and "disloyal".

It was sent by a resident of Avalon Beach on Sydney's northern beaches, and forwarded onto the ABC by one of Prime Minister Julia Gillard's supporters.

"Your determination to destabilise the government and your refusal to unconditionally support Julia Gillard, your leader and our Prime Minister, are despicable," the emailer tells Mr Rudd.

"You delight in half smiles and non-committal responses.

"You really belong in the Liberal Party because you are being so helpful to Tony Abbott's campaign and you don't now really seem to stand for anything but Kevin."

Mr Rudd again attracted attention yesterday by suggesting it was up to the Prime Minister and Treasurer to explain why the mining tax had not raised revenue of any significance.

The tax was renegotiated by Ms Gillard and Wayne Swan soon after she replaced Mr Rudd as prime minister in 2010.

"Your belief in your own infallibility meant that as PM you badly mistimed announcing the mining tax so close to an election instead of awaiting until you had the clear air of three years," the email to Mr Rudd states.

"That bad decision of your is again hurting the Labor Party and your comments this week show again your desire for revenge rather than your loyalty to Labor principles.

"Your disloyalty to your leader and party is shameful. Get over the fact that you are no longer the prime minister."

The email ends with: "I am blind copying this to your Labor colleagues. I know some of them are equally deluded into believing you have a better chance than Julia in winning the election."

Last week, amid reports there was growing support with caucus for him to return to the top job.

Earlier this month he and ultimately the Lodge.