It follows Lord Ashcroft's admission on Monday that he did not pay UK tax on earnings outside Britain, following years of questions from his political opponents.
Labour says he had promised to pay full UK tax when he became a peer in 2000 - Lord Ashcroft says he pledged to "take up permanent residence in the UK".
The 63-year-old is the Tories' deputy chairman and biggest single donor - giving them more than £4m in recent years - and is at the centre of their general election campaign.
He had been turned down for a peerage in 1999 on the grounds that he spent most of his time abroad in Belize and Florida and conducted almost all of his financial matters overseas.
It had been thought he had given assurances he would be resident in Britain for tax purposes when the then Conservative leader William Hague proposed him for a peerage in 2000.
It is unpatriotic - the home secretary claimed - for the Tories to take so much money from a man who chooses not to be a full British taxpayer. If so, all three of the UK's major parties are unpatriotic because they have all taken major sums from so-called non doms
But on Monday Lord Ashcroft said he had only agreed to "take up permanent residence in the UK again" that year and resign as Belize's Special Representative to the UN.
He said that after "subsequent dialogue with the government, it was officially confirmed that the interpretation in the first undertaking of the words 'permanent residence' was to be that of 'a long term resident' of the UK".
He said he had "been declaring all my UK income to HM Revenue" for the past 10 years.
'Shine a light'
Lord Mandelson wrote to the House of Lords appointments commission, which vets parties' nominations for peerages, asking it to "shine a light" on the issue.
But it replied that "the vetting of Lord Ashcroft took place before the commission was established in 2000 and the commission has no documentation on this case and no retrospective powers to investigate".
Lord Mandelson said it was "unacceptable" for the body to refuse to take the matter further.
The questions people have been been asking have now been answered
And Liberal Democrat frontbencher Chris Huhne has written to the chief executive of HM Revenue and Customs, Lesley Strathie, arguing that Lord Ashcroft's "non-dom" status is "incompatible" with him having taken up permanent residence and accepting a peerage for life.
Mr Huhne said his back taxes should be investigated and his non-dom status declared "void".
Meanwhile Conservative MP Greg Hands has put in a Freedom of Information request about Lord Paul - a "non-dom" who has donated money to the Labour Party - relating to his appointment to the Privy Council last year.
Conservative leader Mr Cameron said Lord Ashcroft's statement had settled questions about his tax position and undertakings he gave when he became a peer.
He accused Labour of trying to exploit the issue ahead of the election and said his opponents were "flogging a dead horse" over the issue.
He added: "People have all the information they need, disappointing as it is to some who rather hoped this question could be asked all the way up to polling day."
Lib Dem leader Nick Clegg said it was "wholly wrong" for someone "seeking to influence the outcome of the next general election" to pay taxes "only partially in this country".
But his party has confirmed Tory claims that it has taken donations from three "non-doms" - Bhanu, Sudhir and Dhruv Choudhrie.
An amendment to the Constitutional Reform and Governance Bill, currently going through Parliament and which has all-party backing, will require all MPs and peers to be resident, ordinarily resident and domiciled in the UK for tax purposes.
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